Non-equilibrium capillary electrophoresis of equilibrium mixtures (NECEEM)-based methods for drug and diagnostic development

ABSTRACT

The invention discloses a Non-Equilibrium Capillary Electrophoresis of Equilibrium Mixtures (NECEEM) method and NECEEM-based practical applications. The NECEEM method is a homogeneous technique, which, in contrast to heterogeneous methods, does not require affixing molecules to a solid substrate. The method of the invention facilitates 3 practical applications. In the first application, the method allows the finding of kinetic and thermodynamic parameters of complex formation. It advantageously allows for revealing two parameters, the equilibrium dissociation constant, K d , and the monomolecular rate constant of complex decay, k off , in a single experiment. In the second practical application, the method of this invention provides an approach for quantitative affinity analysis of target molecules. It advantageously allows for the use of affinity probes with relatively high values of k off . In the third practical application, the method of this invention presents a new and powerful approach to select target-binding molecules (ligands) from complex mixtures.

This application is a divisional application of U.S. application Ser.No. 10/610,547, filed Jul. 2, 2003, now U.S. Pat. No. 7,672,786, thecontents of which are herein incorporated herein, in their entirety, byreference.

INCORPORATION OF SEQUENCE LISTING

A computer readable form of the Sequence Listing“13502-6_Sequence_Listing.txt” (1,811 bytes), submitted via EFS-WEB andcreated on Jun. 14, 2010, is herein incorporated by reference.

FIELD OF THE INVENTION

The invention relates to the field of non-equilibrium capillaryelectrophoresis of equilibrium mixtures and the use of the method,particularly in the development of drugs, treatment regimes anddiagnostic methods.

BACKGROUND OF THE INVENTION

Non-covalent molecular complexes play a crucial role in regulatorybiological processes, such as, but not limited to gene expression, DNAreplication, signal transduction, cell-to-cell interaction, and theimmune response. The molecular mechanisms of action of many drugs arebased on drugs forming non-covalent molecular complexes with therapeutictargets. In addition, the formation of non-covalent molecular complexesis pivotal to many analytical techniques and devices used in researchand disease diagnostics, such as, but not necessarily limited to,immunoassays, biosensors, and DNA hybridization analyses (Cepek andBrenner, Nature 1994, 372, 190; Sparks et al. Med. Chem. 1993, 36; Cohenand Williams, Microbiol. Sci. 1988, 5, 265; Pantoliano and Horlick,Biochemistry 1994, 33, 10229; Karlsson, Trends Pharm. Sci. 1991, 12,265; Dalgleish and Kennedy, Vaccine 1988, 6, 215; Christian et al.Biochem. J. 1994, 300, 165).

The formation and decay of a non-covalent complex, L•T, betweenmolecules L (ligand) and T (target), are characterized by a bimolecularrate constant k_(on), and a monomolecular rate constant, k_(off),respectively:

$\begin{matrix}{{L + T}\underset{k_{off}}{\overset{k_{on}}{\rightleftarrows}}{L \cdot T}} & (1)\end{matrix}$where k_(on) is the rate constant of the forward reaction forming L•Tand k_(off) is the rate constant of the reverse reaction. The stabilityof the complex is often described in terms of the equilibriumdissociation constant:K _(d) =k _(off) /k _(on)  (2)The three constants, k_(on), k_(off), and K_(d), are interconnectedthrough equation 2, therefore defining any pair of constants will definethe third. The constants are also dependent on a number of parameters,such as but not limited to buffer composition, buffer pH, buffer ionicstrength, and temperature.

Determination of k_(on), k_(off) and K_(d). Knowledge of k_(on),k_(off), K_(d), and their dependence on certain factors such as buffercomposition, buffer pH, buffer ionic strength, and temperature canassist in: (i) understanding the dynamics of biological processes, (ii)determining the pharmacokinetics of target-binding drugs, and (iii) thedesigning of quantitative affinity analyses. In practical terms thedetermination of k_(on), k_(off), K_(d) can assist in developing and/orselecting drugs with desired kinetic parameters. It may also help indeveloping suitable dosage regimes. In another aspect it can help in thedevelopment of screening and/or diagnostic assays.

Prior art methods for measuring k_(on), k_(off) and K_(d) of a molecularinteraction have significant limitations. The methods that are used forfinding k_(on) and k_(off) can be divided into two broad categories:heterogeneous and homogeneous binding assays. In heterogeneous assays, Tis affixed to a solid substrate, while L is dissolved in a solution andcan bind T affixed to the surface. In advanced heterogeneous bindingassays such as surface plasmon resonance (SPR), T is affixed to a sensorthat can change its optical or electrical signal upon L binding to T(Imanishi and Sugiura, Biochemistry, 2002, 41, 1328; Cheskis andFreedman, Biochemistry, 1996, 35, 3309). In such methods, K_(d) can befound by performing a series of equilibrium experiments. Theconcentration of L in the solution is varied and the interaction betweenL and T is allowed to reach equilibrium. The signal from the sensorversus the concentration of L has a characteristic sigmoidal shape andK_(d) can be found from the curve by identifying the concentration of Lat which the signal is equal to half of its maximum amplitude. Thek_(off) value can be determined by SPR in a single non-equilibriumexperiment in which the equilibrium is disturbed by fast replacing thesolution of L with a buffer devoid of L. The complex on the surfacedecays in the absence of L in the solution, and the complex decaygenerates an exponential signal on the sensor.

Heterogeneous binding assays have certain advantages and drawbacks. Themost serious drawback is that affixing T to the surface changes thestructure of T. The extent of such change will depend on the method ofimmobilization. The change in the structure can potentially affect thebinding parameters of L to T. This problem is especially severe for Lthat binds to T through interaction with a large part of T. In addition,the immobilization of T on the surface may be time-consuming andexpensive. Moreover, non-specific interactions with the surface arealways a concern.

In homogeneous binding assays T and L are mixed and allowed to form acomplex in solution; neither of the molecules are affixed to thesurface. Complex formation is followed by either monitoring the changingphysical-chemical properties of L or T upon binding. Such properties canbe optical (absorption, fluorescence, polarization) orseparation-related (chromatographic or electrophoretic mobility).Equilibrium experiments with varying concentrations of L can be usedsimilarly to heterogeneous analyses to find K_(d). Non-equilibriumstopped flow-experiments, in which L and T are mixed in a fast fashionand the change in spectral properties is monitored, can be used to findk_(on). Non-equilibrium chromatographic experiments, in which acompetitive ligand is added to the chromatographic buffer and allowed tointeract with T was demonstrated to be useful in finding K_(d) andk_(off), although the method involved “non-transparent” numericalanalysis of chromatographic peaks and required an additional reactant,the competitive ligand.

When the quantity of available T or L is a limiting factor, capillaryelectrophoresis (CE) is the method of choice. It requires only nanoliter(nL) volumes of a sample and can detect fewer than 1000 molecules (Wuand Dovichi J. Chromatogr. 1989, 480, 141). Affinity capillaryelectrophoresis (ACE), in which L is added to the run buffer atdifferent concentrations and the change of the mobility of T ismonitored, can be used to determine K_(d) by conducting a series ofequilibrium experiments (Wan and Le, Anal. Chem., 2000, 72, 5583; Le etal., Electrophoresis, 2002, 23, 903; Chu et al. J. Med. Chem., 1992, 35,2915; Chu and Whitesides, J. Org. Chem. 1992, 57, 3524; Carpenter et al.J. Chem. Soc., Chem. Commun. 1992. 804; Chu et al. Cell. and Mol. LifeSci., 1998, 54, 663). However, ACE is an equilibrium approach thatcannot be used for finding k_(off).

Quantitative affinity analyses. Equilibrium binding analyses describedin the previous section can be converted into methods for thequantitative analysis of T using the affinity probe L. Three majorcategories of affinity probes include antibodies (used in immunoassays),DNA hybridization probes (used in analyses of DNA and RNA) (Pease et al.P. Natl. Acad. Sci. USA 1994, 91, 5022; Mullaart et al. Nature, 1993,365, 469; Higuchi et al. Nature, 1988, 332, 543), and aptamers(synthetic affinity probes, e.g. oligonucleotides or oligopeptides)(Clark and Remcho, Electrophoresis 2002, 23, 1335; Li et al. Biochem.Biophys. Res. Commun., 2002, 292, 31; Fredriksson et al. Nat.Biotechnol., 2002, 20, 473). When a target is available in very lowamounts and cannot be amplified (i.e. not subject to PCR), CE can be themethod of choice for developing a quantitative affinity analysis (Coltonet al. Electrophoresis, 1998, 19, 367; Anderson et al. Anal. Chem.,2002, 74, 1870; Tim et al., Electrophoresis, 2000, 21, 220; Heegaard etal., Electrophoresis, 1999, 20, 3122; Busch et al., J. Chromatography A,1997, 777, 311). In CE-based quantitative analyses the mobility shift ofthe affinity probe, L, is measured upon binding to the target, T. Theshift is a function of the concentration of T. One of the majorlimitations of CE is its poor performance for antibodies as affinityprobes. High molecular weight of antibodies significantly limits themobility shift upon binding to a usually smaller target molecule. Recentadvances in developing oligonucleotide aptamers open the possibility oftheir use as affinity probes in CE-based analyses (German et al. Anal.Chem., 1998, 70, 4540). Such analyses have been demonstrated in ACEmode, where the target is added to the buffer. However, ACE has twodrawbacks for quantitative affinity analyses. If the target is aprotein, its addition to the separation buffer is typically associatedwith protein adsorption to capillary walls, which can severely affectthe quality of analysis (Gomez et al., Anal. Chemistry, 1994, 66, 1785).Second, adding the target to the running buffer can be unacceptable ifthe amount of target available is very small. An alternative to the ACEanalysis is: (i) forming the L•T complex out of the capillary andinjecting a small plug of the mixture into the capillary, (ii)separating free L from the L•T complex using a buffer free of T and L,and (iii) monitoring peaks corresponding to L and L•T. However, thismethod is not applicable to L•T complexes with relatively high values ofk_(off) (>10⁻² s⁻¹) since the complex considerably decays during theseparation (the typical separation time is ˜1000 s), which affects theaccuracy of measurements. Many aptamers available today, especiallythose for small-molecule targets, have k_(off) values that do not allowfor their use as affinity probes in such CE-based analyses.

Screening for and selecting drug candidates and affinity probes. Findingnew molecules capable of binding to therapeutic targets is essential forboth drug discovery and development of new diagnostic methods.Target-binding molecules are used as potential drug candidates and asaffinity probes for detecting targets. One of the most efficient ways offinding new target-binding molecules is the screening of complexbiological (e.g. extracts from animal and plant tissues) and synthetic(e.g. combinatorial libraries of compounds) mixtures in binding assays(Chu et al., J. Org. Chem., 1993, 58, 648; Kuntz, Science 1992, 257,1078; Baumbach et al., BioPhrm 1992, 5, 24; Pauwels et al., Nature,1990, 343, 470; Sandler and Smith, Design of Enzyme Inhibitors as Drugs,1989; Zuckermann et al., Proc. Natl. Acad. Sci. U.S.A. 1992, 89, 4605;Fodor et al., Science, 1991, 251, 787; Lam et al., Nature 1991, 354, 81;Whitelegge et al., Am. J. Pharm. Genomics, 2001, 1, 29; Yao et al., J.Pharm. Sci., 2002, 91, 1923; Fortin and Nolan, Chemistry & Biology,2002, 9, 670; Siegel, Current Topics in Medicinal Chemistry, 2002, 2,13; Roberts, Xenobiotica, 2001, 31, 557; Gold, Nat. Biotechnol. 2002,20, 671). Hereafter, the mixture to be screened will be called thesample.

Methods used to screen samples for target-binding molecules (screeningmethods) also fall into two broad categories: heterogeneous andhomogeneous methods. In heterogeneous methods a target is affixed to asolid substrate such as, but not limited to, chromatographic support,beads, filters, walls of microtiter plates, or SPR sensor. The targetcan be affixed to the surface in a number of ways. The target can bechemically immobilized onto the surface or the target can be captured byanti-target antibodies, which are bound to the surface of the solidsubstrate. Also, if the target is a membrane protein, the target can beaffixed to the surface indirectly through cells, which adhere to thesurface. In heterogeneous analyses, the sample is incubated with thetarget. Molecules that bind to the target are captured on the surface.The non-bound components of the sample are washed out and thetarget-binding molecules can then be desorbed and analyzed.Heterogeneous screening methods have a number of drawbacks typical ofheterogeneous analyses in general. The most serious is that affixing thetarget to the surface changes the structure of the target. The extent ofsuch change will depend on the method of immobilization. The change inthe structure can potentially affect binding of molecules to the target.This problem is especially severe when target-binding moleculesrecognize the structure of a large part of the target. In addition, theimmobilization of the target on the surface may be time-consuming andexpensive. Furthermore, non-specific binding to the surface leads to the“contamination” of ligands with non-ligands. In addition all existingheterogeneous screening methods share a very serious limitation. They donot provide a means of screening for target-binding molecules withspecified ranges of binding parameters: k_(on), k_(off), and K_(d).Optimum binding parameters will change from application to application.For example, the k_(on) and k_(off) values of a drug will influence itspharmacokinetics. Depending on the mechanism of a drug's action, themechanism of its side effects, and the desirable regime of itsadministration, different binding parameters will be optimal (Bruice andKahn, Curr. Opin. Chem. Biol., 2000, 4, 540; Van Oss, J. Mol. Recogn.,1997, 10, 203; Schuck, Curr. Opin. Biotechnol, 1997, 8, 498; White etal., Biochemistry, 1988, 27, 91222; Paton and Rang, Adv. Drug. Res.1966, 3, 57). Different binding parameters can also be optimal forligands to be used as affinity probes in different analyses. Forexample, in separation-based affinity analyses, it is desirable thatk_(off) be low to minimize complex decay during separation (German etal. Anal. Chem. 1998, 70, 4540; Berezovski and Krylov, Anal. Chem. 2003,75, 1382). In fast clinical analyses, in contrast, it is essential thatk_(on) values be high to facilitate fast complex formation (VanRegenmortel et al., Immunological Investigations, 1997, 26, 67; Krishnanet al., Env. Health Perspectives, 1994, 102). Other types of analysesmay require specific ranges of K_(d). Thus, it would be very beneficialto have a means of selecting molecules with desirable ranges of k_(on),k_(off), and K_(d).

In homogeneous screening methods, the target is mixed with the sample insolution and then subjected to either electrophoresis or chromatography.The free target is separated from the target-ligand complex based ondifferences in their chromatographic or electrophoretic properties. Themajor advantage of homogeneous screening methods over heterogeneousones, is that they screen for molecules that bind to targets with anunmodified structure.

Despite the well-known advantages of CE, only a few CE-based homogeneousscreening methods are available. Patent WO 97/22000 describes the use ofa CE-based homogeneous screening method to detect compounds present innatural samples that could complex with a known target, as a tool foridentifying potential therapeutic or diagnostic compounds. The methodmonitored changes in the migration pattern of the target duringelectrophoresis as a sentinel of complex formation. Due to thisrequirement, the method is limited to detectable concentrations oftarget and ligand. In addition, this method is limited to detectingcomplexes that remain bound as they migrate past the detector. Theseligands can be referred to as tight binding ligands (TBL). Moderate(MBL) and weak binding ligands (WBL) dissociate before reaching thedetector and do not produce a detectable shift in the migration patternof the target. Hence, they are not detected.

Methods using tight binding competitive ligands (TBCL) were designed toovercome this problem. U.S. Pat. No. 6,299,747 and WO 00/79260 disclosemethods of detecting new therapeutic regulatory and diagnostic compoundsin complex biological materials using a known competitive ligand to thetarget. The TBCL is added to the target/sample mixture and peak changesof the unbound target or the target associated with the TBCL aremonitored alone or together. MBLs and WBLs in the sample mixture thatresult in an increased unbound peak or a decreased target/TBCL peak, aredetected. The patent indicates that MBLs and TBLs are detectable in thepicomolar (pM) to low nanomolar (nM) range. This method, however,requires that a known TBCL exist and be available, and is limited toembodiments using detectable concentrations of target since the methodrelies on tracking changes in the migration pattern of the target.Homogeneous methods employing CE have also been combined with analyticalmethods to aid in the identification of target binding ligands. WO00/03240 describes a method where the CE technique is combined with massspectrometry, for screening complex samples. Again this method relies oncomplexes that migrate stably through the CE instrument.

Furthermore attempts have been made to select ligands that bind thechosen target with a selected binding strength. WO 99/34203 provides amethod for determining relative binding strengths of ligands that bindthe chosen target. This permits ligands to be ranked according to theirrelative binding strengths, which can aid in prioritizing furtheranalysis. This method, however, does not provide a means of obtainingreal binding parameters as the terms “affinity” and “relativeaffinities” are used in this patent “in a general sense, and do notnecessarily refer to a hit compound's “binding affinity” to a target inan equilibrium situation”.

To conclude, the existing CE-based homogeneous screening methods (WO97/22000, U.S. Pat. No. 6,299,747, WO 00/79260 and WO 00/03240) shareseveral serious disadvantages. They all require: (i) detectable amountsof target and (ii) large amounts of ligands capable of inducingdetectable shifts of the peak of target. Due to the first requirementthey are unable to select ligands for targets present in small amountsand ligands with specified binding parameters. The second requirementmakes it impossible to screen for ligands that constitute only a verysmall portion of the screened sample, such as components of a largecombinatorial library where ligand representation is low. Indeed, therelative amount of ligands, which have required binding parameters incombinatorial libraries can be as low as 10⁻¹³ (Gold, J. Biol. Chem.270, 1995, 13581) such that the target-ligand complexes will be presentin undetectable amounts, and will not introduce a mobility shift to thetarget. Finally, the existing CE-based homogeneous screening methods donot provide a means of selecting ligands with a specified range ofk_(on), k_(off), and K_(d) parameters.

SUMMARY OF THE INVENTION Introduction

The present invention provides a Non-Equilibrium CapillaryElectrophoresis of Equilibrium Mixtures (NECEEM)-based method fordetermining and using equilibrium and/or kinetic parameters of complexformation between two components, such as of a bimolecular interaction.In a preferred embodiment, the method is a homogeneous method. Inanother embodiment, the method can be used to screen for selectingcomponents of a bimolecular interaction that have specified kinetic orbinding parameters, such as in drug screening. In another embodiment,the invention can be used to determine the concentration of one or moreof the components of the complex. In another embodiment, the method ofthe invention can be used to determine the thermodynamic parameters of abimolecular interaction.

In one embodiment, the method of the invention allows for finding K_(d),k_(off), and/or k_(on) for complex formation from a singleelectropherogram. In one embodiment, the invention provides a method forfinding one, two or all three of said parameters. In one embodiment, themethod is a homogenous method. In another embodiment, the components areL and T and the complex is L•T. In yet another embodiment of the method,an equilibrium mixture of said components and complex is subjected tocapillary electrophoresis under non-equilibrium conditions. Thecomponents and complex are separated by size and charge and detected ata detection point by a detector. The mode of detection can depend on theproperties of the components and complex and how or whether thecomponents are labeled. For instance, in one embodiment, one of thecomponents can be fluorescently labeled. In another embodiment, thecomponents and complex can be detected using their native lightabsorption or fluorescence or electrochemical properties or anycombination of them.

The detector can be selected from a variety of types of detectors. Inone embodiment, the detector is a UV absorbance detector, which isstandard on commercial CE instruments. Many instruments also have diodearray detectors available. Alternative detector modes includefluorescence laser-induced fluorescence, and electrochemical detection.

As the components and complex pass through the detector, the time ofpassage can be recorded to form an electropherogram containing peakscorresponding to the components and complex and exponential curvescorresponding to the decay of the complex. However, other methods forrecording time of passage of components, complex and rate of decay couldalso be used. For instance, a detector can be employed that images alarge portion or whole length of the capillary. In one embodiment, thepeaks and area under the curves in the electropherograms can be used todetermine relative amounts of the detected component(s) and/or complex,and can be used to form calibration curves and peaks when known amountsof component(s) and/or complex are present. In another embodiment, thesecalibration curves and peaks can then be used to determine theconcentrations or relative amounts of the components and/or complex inmixtures where these concentrations or relative amounts are not known.In another embodiment the concentration of a component can be determinedby first establishing the equilibrium dissociation constant of thebimolecular interaction of the components and using the dissociationconstant to determine the unknown concentration of the component. In oneembodiment, the complex only slightly decays, considerably decays orcompletely decays during NECEEM.

In one embodiment of the invention, only one of the components isdetected. In another embodiment both components are detected.

In one embodiment, the CE is coupled directly to another device, such asa thermocycler or a mass spectrometer. The hyphenation of CE and massspectrometers is frequently used to give structural information on theresolved peaks. In another embodiment, the detectors can be interfacedwith data acquisition devices to process results.

The peaks and curves of the resulting electropherograms can be used todetermine the kinetic parameters of the complex or bimolecularinteraction.

In one embodiment the equilibrium mixture is prepared in anelectrophoresis run buffer. In another embodiment, the run buffer isfree of said components and complex. In another embodiment the runbuffer is optimized to separate the complex from said components incapillary electrophoresis. In another embodiment the run buffer containsa mediator that enhances electrophoretic separation of the complex fromcomponents.

In one embodiment the method of the invention can be used to determinethe temperature of said capillary. This can be done by measuring theequilibrium and/or kinetic parameters of complex formation at differenttemperatures of said equilibrium mixture and/or said capillary.Thermodynamic parameters, such as enthalpy, the change of entropy andactivation energies of the formation and decay of said complex can bedetermined. Calibration parameters can be determined at knowntemperatures and can be used to determine unknown temperatures.

In yet another embodiment, the invention provides a method selecting aligand, L, that binds the target, T, with specified binding parameters,K_(d), k_(on), and/or k_(off) of the formation of complex between theligand and target using the aforementioned method for determining saidkinetic parameters. In one embodiment, the ligand can be selected from asample comprising a plurality of ligands with different bindingparameters. In another embodiment, more than one ligand can be selected.In yet another embodiment, the method comprises:

-   -   (a) preparing and equilibrating, e.g. incubating, a mixture        comprised of said sample and target, wherein the concentration        of said target and the time of said equilibration are defined by        the desired values of: (i) the equilibrium dissociation        constants of said complex and (ii) the bimolecular rate constant        of the formation of said complex;    -   (b) subjecting said equilibrium mixture to capillary        electrophoresis, such as by injecting a plug of said equilibrium        mixture into a capillary filled with the buffer solution free of        the components of said sample, wherein said capillary is a part        of the capillary electrophoresis instrument, wherein said buffer        solution is the electrophoresis run buffer; wherein said run        buffer is optimized to separate said sample from said target;        wherein such run buffer is optimized not to separate the        components of said sample and applying voltage to the ends of        said capillary and subjecting the components of said equilibrium        mixture to capillary electrophoresis;    -   (c) collecting fractions eluting from said capillary in        different time windows, wherein said time window defines the        values of said binding parameters.        In one embodiment, the buffer solution is free of said target.        In another embodiment, said buffer solution contains said        target. In one embodiment, the fraction is collected in a        specific time window in said electrophoresis. In another        embodiment, said time window excludes the electrophoretic peak        of said sample, yet in another embodiment, the time window        includes the electrophoretic peak of said sample.

In yet another embodiment, said time window includes the electrophoreticpeak of said complex.

In one embodiment, the sample is a biological sample. In anotherembodiment, the sample is a combinatorial library, such as a library ofoligonucleotides. In another embodiment, aptamers are selected from saidlibrary.

In yet another embodiment, the run buffer contains a mediator, whichenhances electrophoretic separation of the components of said samplefrom said complex.

In another embodiment, the method of the invention is applied to thesample that was pretreated prior to the preparation of the equilibriummixture, such as by the enrichment of the sample with the ligands usinganother binding assay. In one embodiment, the sample is a library ofoligonucleotides and the binding assay is a heterogeneous method ofenriching the population of oligonucleotides ligands in the library.

In another embodiment, the method of the invention is applied to amixture of targets. In another embodiment, the complexes of the ligandsand targets have different migration times in capillary electrophoresis.In another embodiment, the complexes are collected in different timewindows in capillary electrophoresis. In yet another embodiment, thecomplexes are identified using another analytical method, for example,but not limited to one of the following: immunoassay, liquidchromatography, affinity chromatography, capillary affinityelectrophoresis, and mass spectrometry.

In one embodiment, the migration time of the target is determined in aseparate capillary electrophoresis run.

In yet another embodiment the capillary in the aforementioned methods ofthe invention is a channel of a microfabricated device.

In another embodiment the target is a protein, for example proteinfarnesyltransferase.

In one embodiment of the methods of the invention, the inner surface ofthe capillary is coated.

In one embodiment of the methods of the invention a mediator added tothe buffer to enhance separation is a nucleic-acid binding protein, suchas a single-stranded DNA binding protein.

Further Embodiments

In one embodiment, the method is realized in the following way. Thecomplex-forming components are allowed to react and form an equilibriummixture. This can be done either outside or inside the capillary. If theequilibrium mixture is prepared outside the capillary, a plug of theequilibrium mixture is introduced into the capillary and subjected tocapillary electrophoresis under non-equilibrium conditions to permitcomplex decay and separation of the components and complex. Themigration of one or more components and the complex is monitored. In oneembodiment, the migration of the components and complex are detected ata detection point to generate an electropherogram that includes peaksand curves, the areas under which represent the amounts of componentsand/or complex that have passed through said detection point in acertain time interval. In a preferred embodiment, this singleelectropherogram may contain enough data to obtain all the kineticparameters. However, a person skilled in the art would appreciate thatany detector monitoring system can be used that enables thedetermination of amounts (actual or relative) of the components andcomplex, and rate of decay over time. In a preferred embodiment, thevalue of K_(d) can be calculated from the areas under electrophoreticpeaks and curves using one of the following two equations:

$K_{d} = \frac{A_{L}A_{T}}{A_{L \cdot T} + A_{decay}}$$K_{d} = \frac{{\lbrack T\rbrack_{0}\left( {1 + \frac{A_{L}}{A_{L \cdot T} + A_{decay}}} \right)} - \lbrack L\rbrack_{0}}{1 + {1/\frac{A_{L}}{A_{L \cdot T} + A_{decay}}}}$wherein A_(T), A_(L), and A_(L•T) are areas of peaks corresponding tocomplex-forming components named T and L, and complex L•T, respectively;A_(decay) is the area under the curve corresponding to the decay ofcomplex L•T. [T]₀ and [L]₀ are total concentrations of the twocomponents in the equilibrium mixture. The areas are normalized withrespect to specific detection properties of T and L, such as extinctioncoefficients, quantum yields, and electrochemical potentials. The firstequation is applicable to cases when both L and T are detectable. Thesecond one is applicable to cases when only one component, L, isdetectable. Then in this embodiment, the value of k_(off) can bedetermined by fitting the decay curve with a single-exponentialfunction:

$I_{t} = {I_{t_{0}}\exp\left\{ {k_{off}\frac{t_{L \cdot T}}{t_{C} - t_{L \cdot T}}\left( {t - t_{0}} \right)} \right\}}$If the fitting is impossible due to contamination of the components thatcauses additional peaks in the area of the decay curve, then k_(off) canbe calculated based on the analysis of the areas:

$k_{off} = \frac{\ln\left( {\left( {A_{L \cdot T} + A_{decay}} \right)/A_{L \cdot T}} \right)}{t_{L \cdot T}}$In the last two formulas, t₀ and t are initial and variable time pointson the decay curve of L•T; t_(C) is the migration of one of thecomponent, whose signal constitutes the curve; t_(L•T) is the migrationtime of L•T capillary electrophoresis. Finally, k_(on) can be determinedusing the following equation:k _(on) =k _(off) /K _(d)The method is applicable to components of different nature and origin.For example, a component can be an organic molecule, protein, peptide,enzyme, nucleic acid, aptamer, organelle, cell, virus, particle, orother reagent separable by capillary electrophoresis. If necessary, thecomponent may be pretreated using different procedures such as, but notlimited to: lysis, freeze-thaw, centrifugation, enrichment orfractionation. The components can be detected using light absorption,fluorescence, electrochemical properties, radioactivity, mass or chargeproperties. If the component is not detectable it can be labeled with atag that facilitates one of the listed above modes of detection. Theelectrophoresis parameters are optimized to facilitate separation of thecomponents from the complex. This optimization can include modificationsto the voltage, temperature, buffer composition (includingseparation-enhancing mediators), buffer pH, capillary dimensions(including length, inner and outer diameters, material the capillary ismade of, capillary pretreatment such as siliconization. If kineticparameters are measured at different temperatures, then thermodynamicparameters, such as reaction enthalpy, the change of entropy, andactivation energies of the formation and decay of the complex can bedetermined by a person skilled in the art of CE. These thermodynamicparameters can further serve as an indicator of temperature in anelectrophoresis device, in which temperature is not controlled.

In another embodiment, the method of the invention allows for thedetermination of an unknown concentration of target (T) molecules usingCE and affinity probe (L) whose complexes with the target moleculesdecay partially or completely during the CE process. First, the K_(d)value of complex formation between T and L is determined as described inthe previous paragraph, using known concentrations of T and L. Then, anequilibrium mixture comprised of an unknown concentration of T and aknown concentration of L is subjected to CE under non-equilibriumconditions optimized by the operator to separate the complex L•T from L.The electropherogram that may contain peaks of L and L•T and a curvecorresponding to the decay of L•T are analyzed to determine the unknownconcentration of T:

$\lbrack T\rbrack_{0} = {{K_{d}/\frac{A_{L}}{A_{L \cdot T} + A_{decay}}} + {\lbrack L\rbrack_{0}/\left( {1 + \frac{A_{L}}{A_{L \cdot T} + A_{decay}}} \right)}}$where A_(L) and A_(L•T) are the areas under the peaks corresponding to Land L•T, respectively A_(decay) is the area under the curvecorresponding to the decay of L•T during capillary electrophoresis; [T]₀and [L]₀ are total concentrations of the two components in theequilibrium mixture. T can be, for example, an organic molecule,protein, peptide, enzyme, nucleic acid, aptamer, organelle, cell, virus,particle, or other reagent separable by capillary electrophoresis. L canbe any chemical entity that binds the target with required specificityand affinity. If necessary, T may be pretreated using differentprocedures such as, but not limited to: lysis, freeze-thaw,centrifugation, enrichment or fractionation. L can be detected usinglight absorption, fluorescence, electrochemical properties,radioactivity, mass or charge properties. If L is not detectable it canbe labeled with a tag that facilitates one of the above listed modes ofdetection. The electrophoresis parameters are optimized to facilitateseparation of L from L•T. This can include modifications to the voltage,temperature, buffer composition (including separation-enhancingmediators), buffer pH, capillary dimensions (length, inner and outerdiameters), capillary material, or capillary pretreatment such assiliconization. Alternatively to measuring K_(d), a calibration curveA_(L)/(A_(L•T)+A_(decay)) vs. [T] can be built. The method can be usedas a diagnostic tool to measure the concentration of T present in apatient or biological sample.

In another embodiment, the method of the invention allows for screeningand selecting target (T) binding molecules (L), in a fashion thatovercomes some of the previously listed problems with using CE. Inparticular, the method of the invention allows for: (i) selecting L witha specified range of K_(d), k_(off), and k_(on) values and/or (ii)selecting L when L constitutes only a very small fraction of the totalsample and/or (iii) selecting L when T is only available in very smallamounts. In one embodiment, the method is realized as follows. First, anequilibration mixture comprised of a sample and T is prepared outside orinside the capillary. The concentration of T and the time ofequilibration are defined by the operator depending on the desiredvalues of K_(d) and k_(on). In the initial selection, ligands withK_(d)<K_(d) ^(max)=[T]₁ and k_(on)>k_(on) ^(min)=1/[T]₁t_(eq1) areselected. To achieve this, the equilibrium mixture contains aconcentration of T equal to [T]₁ and is equilibrated for time equal tot_(eq1). In the following step the ligands with K_(d)>K_(d) ^(min)=[T]₂and k_(on)<k_(on) ^(max)=1/[T]_(eq2) are selected. To achieve this, theequilibrium mixture contains a concentration of T equal to [T]₂ and isequilibrated for time equal to t_(eq2). In general, [T]₂<[T]₁ andt_(eq2)<t_(eq1). If the equilibrium mixture is prepared outside thecapillary, a plug of the mixture is introduced into the capillary andsubjected to capillary electrophoresis under non-equilibrium conditions.The electrophoresis conditions are optimized to separate the sample fromT but not to separate the components of the sample. Fractions elutingfrom said capillary are collected at different time windows, whichdefine the values of K_(d), k_(on), and k_(off) of the collectedligands. T can be an organic molecule, protein, peptide, enzyme, nucleicacid, aptamer, organelle, cell, virus, particle, or other reagentseparable by capillary electrophoresis. L can be any chemical entitythat binds the target with the required specificity and affinity. L maybe a component of a biological sample, patient sample, combinatoriallibrary or other complex mixture. If necessary, T and the sample may bepretreated using different procedures such as, but not limited to:purification, enrichment, fractionation, lysis, freeze-thaw, andcentrifugation. Advantageously, T does not need to be detectable. L andthe other components of the sample can be detected using lightabsorption, fluorescence, electrochemical properties, radioactivity,mass or charge properties. If L is not detectable it can be labeled witha tag that facilitates one of the above listed modes of detection. Theelectrophoresis parameters are optimized to facilitate separation of Lfrom L•T. This optimization can include modifications to the voltage,temperature, buffer composition (including separation-enhancingmediators), buffer pH, capillary dimension (length, inner or outerdiameter) capillary material, or capillary pretreatment such assiliconization. When the sample is a combinatorial library ofoligonucleotides, the method of the invention can be used to selectaptamers that bind T with specific K_(d), k_(on) and k_(off) values. PCRamplification of collected fractions can be used to amplify collectedaptamers. For example, the method of the invention was used to selectaptamers to protein farnesyltransferase. When selecting aptamers fromoligonucleotide libraries, a single-stranded DNA-binding protein can beused to facilitate the separation of single stranded oligonucleotidesfrom the aptamer-target complexes. When the sample is a combinatoriallibrary containing potential therapeutic agents, the method of theinvention can be used to select drug candidates or diagnostic probesthat bind the therapeutic target with specific K_(d), k_(on) and k_(off)values. When the sample is a biological sample, the method of theinvention can be used to select natural agents capable of binding T withspecific K_(d), k_(on) and k_(off) values. The method of the inventioncan be applied to individual or multiple targets. To characterize theselected L, other analytical methods, such as immunoassay, liquidchromatography, affinity chromatography, capillary affinityelectrophoresis, PCR, or mass spectrometry can follow the method of theinvention. To further improve the efficiency of such combined methods ananalytical device can be directly attached to the CE instrument. In afurther embodiment, the method of the invention can be performed underequilibrium conditions when the electrophoresis buffer contains T. Toconclude, the method of the invention advantageously allows blindselection of ligands when the concentrations of the target and ligandsare below the limit of detection. The invention can be utilized even ifonly single molecules of ligand or target are present, as theirdetection is not required. This flexibility is essential for selectingligands with desirable K_(d), k_(on) and k_(off) values as well as forselecting ligands when T is only available in small amounts or when Lrepresents only a small fraction of the total sample, such as aptamersselected from a combinatorial library (a candidate aptamer mayconstitute as low as 10⁻¹³ of the sample (Gold, J. Biol. Chem. 270,1995, 13581).

Other features and advantages of the present invention will becomeapparent from the following detailed description. It should beunderstood, however, that the detailed description and the specificexamples while indicating preferred embodiments of the invention aregiven by way of illustration only, since various changes andmodifications within the spirit and scope of the invention will becomeapparent to those skilled in the art from this detailed description.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a schematic representation of NECEEM electropherograms whenboth L and T are detectable. Panels A, B and C correspond to low,intermediate, and high k_(off) values, respectively. Due to undetectablecomplex decay in panel A, NECEEM converges into an ordinary equilibriumCE.

FIG. 2 is a schematic representation of NECEEM electropherograms whenonly L is detectable. Panels A, B and C correspond to low, intermediate,and high k_(off) values, respectively. Due to undetectable complex decayin panel A, NECEEM converges into an ordinary equilibrium CE.

FIG. 3 is a schematic representation of a NECEEM electropherogram duringthe selection of ligands with K_(d)<K_(d) ^(max)=[T]₁ and k_(on)>k_(on)^(min)=1/[T]₁t_(eq1) when the migration time of the target is unknown.Ligands are selected from both sides of peak L, corresponding to thesample.

FIG. 4 is a schematic representation of a NECEEM electropherogram duringthe selection of ligands with K_(d)<K_(d) ^(max)=[T]₁ and k_(on)>k_(on)^(min)=1/[T]₁t_(eq1), when the migration time of the target is known.Ligands are collected between t_(T) and t_(L) from one side of peak L,which corresponds to the sample. They are collected to the left of peakL, if t_(T)<t_(L) (Panel A) and to the right of peak L, if t_(T)<t_(L)(Panel B).

FIG. 5 is a schematic representation of a NECEEM electropherogram duringthe selection of ligands with K_(d)>K_(d) ^(min)=[T]₂ and k_(on)<k_(on)^(max)=1/[T]₂t_(eq2). Panels A to C demonstrate examples using differentvalues of [T]₂ with respect to [T]₁, and t_(eq2) with respect tot_(eq1). Panel A illustrates the case when most of the ligands in thepool bind to T and are observed either as peak L•T or its exponentialdecay. Panel B illustrates the case when little of the fraction ofligands is bound to T so that peak L•T and its decay are not detectable.Panel C illustrates the case when comparable amounts of the ligands bindto T and are present in a non-bound state so that the areas of peak Land peak Da along with its decay are comparable.

FIG. 6 is a schematic representation of a NECEEM electropherogram duringthe selection of ligands with k_(off)<k_(off) ^(max)=1/t_(L•T) (PanelA), and 1/t₂=k_(off) ^(min)<k_(off)<k_(off) ^(max)=1/t₁ (Panel B).

FIG. 7. Panel A schematically represents the electropherogram of aselection of ligands from a sample where the ligands are in very lowabundance, using a run buffer that contains the target at concentration[T]_(buf). Panel B represents a schematic Scotchard plot for the ligandwith K_(d)=[T]_(buf).

FIG. 8 depicts the use of a NECEEM-based method for determining theK_(d), k_(off), and k_(on) values of complex formation between an SSBprotein and a fluorescently labeled 15-mer oligonucleotide,5′-fluorescein-GCGGAGCGTGGCAGG (SEQ ID NO:1) (fDNA). The totalconcentrations of the components in the equilibrium mixture are:[SSB]₀=0.32 μM and [fDNA]₀=0.16 μM. The run buffer was 25.0 mM borate atpH 9.4. The inset illustrates the fitting of the exponential part with asingle-exponential function.

FIG. 9 illustrates the use of a NECEEM-based method for determining theK_(d), k_(off), and k_(on) values of complex formation between the Mef2cprotein and a fluorescently labeled dsDNA of the following sequence:CCTGCCACGCTCCGCTCTAAAAATAA (SEQ ID NO:2). The total concentrations ofthe components in the equilibrium mixture were: [Mef2c]₀=1.0 μM and[dsDNA]₀=0.1 μM. The run buffer was 25.0 mM tetraborate at pH 9.4.

FIG. 10 illustrates the use of a NECEEM-based method for determining theK_(d), k_(off), and k_(on) values of complex formation between Taq DNApolymerase and its fluorescently labeled aptamer. Panel A shows theseparation of excess fDNA from the aptamer-fDNA hybrid. Panel Billustrates a NECEEM electropherogram for the Taq DNA polymerase•aptamercomplex. The total concentrations of the components in the equilibriummixture were: [Taq DNA polymerase]₀=5 nM and [Aptamer]₀=50 nM. The runbuffer contained 100 nM SSB in 25.0 mM tetraborate at pH 9.4.

FIG. 11 depicts the use of a DNA-binding protein, SSB, in a NECEEM-basedmethod for determining the K_(d), k_(off), and k_(on), values of complexformation. SSB enhances separation of ssDNA from dsDNA, aiding in thedetermination of equilibrium and kinetic parameters of DNA hybridizationcomplex formation (SEQ ID NOS: 1, 2 and 5).

FIG. 12 illustrates the use of a NECEEM-based method for determiningthermodynamic parameters of complex formation between SSB and fDNA.Panel A is a typical NECEEM electropherogram. Panel B illustrates thedependence of k_(off) on temperature while Panel C illustrates thedependence of K_(d) on temperature.

FIG. 13 illustrates the use of a NECEEM-based method for determining anunknown concentration of thrombin using its aptamer.

FIG. 14 shows a capillary electrophoresis of 1 μM PFTase detected usinglight absorption at 280 nm.

FIG. 15 illustrates the use of a NECEEM-based method for blind selectionof oligonucleotide aptamers to PFTase from a combinatorial library ofoligonucleotides. Panel A illustrates step 1 in the selection: Afraction from the equilibrium mixture, of the library and PFTase (1 μM),is collected blindly (neither PFTase or the PFTase•aptamer complexes aredetectable) from a wide window to the left of the peak of the library.Panel B illustrates step 2 in the selection: A fraction from theequilibrium mixture, of the fraction from step 1, subjected to PCRamplification, and PFTase (1 μM), is collected in a fashion similar tothat in step 1. Panel C illustrates the peaks of PFTase•aptamercomplexes in the equilibrium mixture, of a PCR-amplified fraction fromstep 2 and PFTase (1 μM). Two steps of blind selection were sufficientto select aptamers. Panel D illustrates a control electropherogram: APCR-amplified fraction from step 2 without PFTase.

FIG. 16 shows a NECEEM electropherogram of aptamer•PFTase complexes in abuffer that contains 100 nM SSB as a mediator for separating fDNA (usedto fluorescently label aptamers and other oligonucleotides of thelibrary) and non-bound oligonucleotides, from the complexes of aptamersand targets. Panel A illustrates an electropherogram of a PCR-amplifiedfraction from step 2 (see FIG. 15). Panel B shows a NECEEMelectropherogram of a PCR-amplified fraction from step 2 with 1 μMPFTase.

DETAILED DESCRIPTION OF THE INVENTION Definitions

ACE—affinity capillary electrophoresis, the mode of capillaryelectrophoresis in which one of the complex-forming components is addedto the separation buffer to maintain the equilibrium during the courseof CE separation.

Aptamer as used herein means a binding partner that is selected from acombinatorial library that is nucleotide- or peptide-based. Aptamers arecharacterized by high selectivity and high affinity towards the targetsthey are selected for. Due to these properties aptamers are often viewedas artificial antibodies.

Bimolecular interaction is a reaction between 2 chemical entities orcomponents. Each entity can itself comprise more than one component. Thepairs of interacting entities include but are not limited to: proteinand protein, protein and nucleic acid, protein and aptamer, enzyme andsubstrate, antigen and antibody, drug and therapeutic target, affinityprobe and diagnosed molecule, hybridization probe and target nucleicacid sequence, etc.

CE—capillary electrophoresis

Combinatorial library as used herein means a collection of syntheticcomponents that are produced by randomized synthesis. For example,combinatorial libraries of oligonucleotides or peptides consist ofoligonucleotides or peptides of randomized sequence compositions.Combinatorial libraries can also be comprised of small organic moleculesof randomized structure. The library can comprise multiple differentligands or targets. They can be from a biological sample. In oneembodiment, the library is a library of chemical compounds, organicmolecules, peptides, or nucleic acids.

Component as used herein refers to a chemical entity or substance thatcan interact with at least one other chemical entity or substance toform a complex comprising two components. Each entity itself cancomprise one or more

dNTP—deoxynucleotide triphosphate

dsDNA—double stranded deoxyribonucleic acid

Dynamic range as used herein means the range of concentrations of targetwithin which the method works.

Electropherogram as used herein means the time-dependent signal producedin a capillary electrophoresis. The signal is sensed by a detectorplaced at a certain point along the length of the capillary or past thecapillary. The intensity of the signal, when properly normalized, isproportional to the concentration of detected species. The integratedsignal (or the area under the line in the electropherogram) for the timewindow t₁-t₂ represents the amount of the species that passed thedetector in this time window.

t_(eq)—Equilibration time as used herein means incubation time of theequilibrium mixture from the point of mixing components to the beginningof NECEEM. Equilibration time defines the ligands that are capable ofbinding the target. The ligands with k_(on)>1/[T]t_(eq) will preferablyequilibrate with the target within equilibration time t_(eq), whilethose with k_(on)<1/[T]t_(eq) will not reach equilibrium.

Equilibrium as used herein relates to the reaction of complex formationand means a state wherein the rate of complex formation is equal tocomplex decay so that the concentration of the components and complex donot change with time. Conditions that facilitate the maintenance ofequilibrium are said to be equilibrium conditions. An equilibriummixture or equilibrium composition as used herein refers to acomposition comprising both components and the complex in a state ofequilibrium (i.e. where the concentrations remain relatively stable orunchanged over time).

fDNA—is a fluorescently labeled DNA, such as5′-fluorescein-GCGGAGCGTGGCAGG (SEQ ID NO:1).

Heterogeneous Assay as used herein is an assay wherein on of theinteracting components is affixed to a solid substrate. In this case theinteraction between the components is realized on the surface. Since theconcentration of the affixed component on the surface is not defined,many aspects of standard kinetics are not applicable to heterogeneousassays. component on the surface is not defined, many aspects ofstandard kinetics are not applicable to heterogeneous assays.

Homogeneous Assay as used herein is an assay wherein the components formcomplexes in solution and neither of the interacting components (targetand ligand) is affixed to a solid substrate. Standard homogeneouskinetics based on the concentration of the components is applicable tohomogeneous assays.

I.D.—inner diameter

K_(d) as used herein means the equilibrium dissociation constant of acomplex measured in mol/L or M.

k_(off) as used herein means the monomolecular rate constant of complexdecay measured in s⁻¹.

k_(on) as used herein means the bimolecular rate constant of complexformation measured in mol⁻¹ Ls⁻¹ or M⁻¹ s⁻¹.

kPa—kilopascals

kV—kilovolts

L—ligand as used herein, in very general terms means one of twointeracting components (the second component is called target herein).In one embodiment a ligand can be either the affinity probe, or atarget-binding molecule, which is selected from a sample. For example,an aptamer selected from a combinatorial library of oligonucleotides isa ligand, while the molecule which the aptamer binds specifically, isits target. Another example of a ligand is a drug candidate that bindsits therapeutic target. In another embodiment, it can be, but is notnecessarily limited to a molecule, protein, nucleic acid, aptamer,organelle, virus, bacterium, cell, particle or combination thereof.

[L]—concentration of L

L•T—dynamic complex of L and T

Large Combinatorial Library as used herein is a combinatorial library inwhich the probability of any molecule to be unique is greater than 99%.

Microfabricated device as used herein is a device that contains amicro-channel, which can serve as a capillary for CE.

Migration time as used herein means the time required by a chemicalentity subjected to CE, to reach the detector. Migration time isinfluenced by a number of parameters, such as electric field,composition and pH of CE run buffer, modification of capillary walls,etc.

NECEEM—Non-equilibrium capillary electrophoresis of equilibrium mixturesis capillary electrophoresis, in which an equilibrium composition ofcomponents and complexes are subjected to electrophoresis underconditions that promote decay of the complexes loaded therein.

Non-equilibrium as used herein refers to a state wherein the componentsand complex of a reaction are not in equilibrium, such thatconcentrations of each of the components and complex are not stable,e.g. in a state of fluctuation. Conditions that cause the equilibriumnot to be maintained are said to be non-equilibrium. For example,conditions that promote decay of a complex are non-equilibriumconditions; under such conditions the concentration of the complex isdecreasing while the concentration of free components is increasingduring the decay process over time. Non-equilibrium conditions can beinduced by the removal of one or more components from the equilibriummixture.

O.D.—outer diameter

PCR—polymerase chain reaction

PFTase—protein farnesyltransferase

Plug as used herein means the solution injected into the capillary

psi—pounds per square inch

Sample as used herein means a composition that can be natural,biological or synthetic that may contain potential ligands.

SSB—single-stranded DNA binding protein from E. coli

ssDNA—single stranded deoxyribonucleic acid

T—target as used herein, means one of two interacting components (thesecond component is called ligand herein). In one embodiment it can beeither the component whose concentration is to be determined, or thecomponent for which another component (ligand) is to be selected from asample. For example, a therapeutic target is a molecule, such asprotein, with which a drug candidate can target can be, but is notnecessarily limited to a molecule, protein, nucleic acid, aptamer,organelle, virus, bacterium, cell, particle or combination thereof.

[T]—concentration of T

t_(C)—migration time of one of components (C)

t_(L)—migration time of L

t_(T)—migration time of T

t_(L•T)—migration time of L•T

DESCRIPTION

Capillary electrophoresis (CE) has proved to be a very efficientanalytical tool exhibiting high resolution, high sensitivity, highspeed, and requiring only minimal amounts of sample. The method of thisinvention is based on a new CE approach, termed Non-EquilibriumCapillary Electrophoresis of Equilibrium Mixtures (NECEEM). NECEEM isbased on the inventors' finding that the advantages of equilibrium andnon-equilibrium conditions can be combined in a single capillaryelectrophoresis procedure to provide the foundation of three practicalapplications. Conceptually in NECEEM, an equilibrium mixture ofmolecules T (Target) and L (Ligand), is prepared by mixing them andallowing them, outside or inside the capillary, to reach equilibrium asdescribed by equation 1:

$\begin{matrix}{{L + T}\underset{k_{off}}{\overset{k_{on}}{\rightleftarrows}}{L \cdot T}} & (1)\end{matrix}$

The concentrations of L, T, and L•T in the equilibrium mixture aredefined by K_(d). If the equilibrium mixture is prepared outside thecapillary, a plug of the mixture is introduced into the capillarypreferentially by pressure (electrokinetic introduction can disturbequilibrium) and subjected to electrophoresis under non-equilibriumconditions, using a separation buffer. In one embodiment, the separationbuffer contains neither L nor T. The separation conditions are optimizedso that at least two of the three components L, T and L•T, areeffectively separated. Under such conditions at least one of L and T iscontinuously removed from the electrophoretic zone of L•T and suchremoval causes continuous monomolecular decay of L•T with the rateconstant k_(off). Electrophoretic data generated by NECEEM arecomprised, in general, of three peaks and two curves (FIG. 1). Two peakscorrespond to equilibrium fractions of L and T and one peak tonon-decayed L•T. The curves correspond to L and T produced by the decayof L•T. The number of peaks and curves may be fewer if only one of thetwo components, L or T, is detectable (e.g. has a fluorescent label orother detectable property or label (see examples 2 and 8)), or if L•Tdecays to undetectable levels upon reaching the detector (see examples1C, 2C, 9, and 13). Due to the mixed equilibrium/non-equilibrium natureof NECEEM, the electrophoretic data contains accurate information aboutboth K_(d) and k_(off). This feature of NECEEM forms the basis of theapplications disclosed in this application.

This document discloses three practical applications of the NECEEM-basedmethod. In the first application, the method of the inventionfacilitates finding kinetic and thermodynamic parameters of complexformation. It advantageously allows for revealing two parameters, theequilibrium dissociation constant, K_(d), and the monomolecular rateconstant of complex decay, k_(off), from a single electropherogram. Inthe second application, the method of the invention provides an approachfor quantitative affinity analysis of target molecules. It facilitatesthe use of affinity probes with relatively high values of k_(off)(k_(off)>10⁻² s⁻¹) in such analyses. In the third practical application,the method of this invention presents a new and powerful approach toselect target-binding molecules (ligands) from complex mixtures. Uniquecapabilities of the method of the invention with respect to the thirdapplication include but are not limited to: (a) the selection of ligandswith specified ranges of kinetic and thermodynamic parameters oftarget-ligand interactions, (b) the selection of ligands present inminute amounts (even as low as 1 molecule) from complex mixtures ofbiological or synthetic samples, and (c) the selection of ligands fortargets available in very low amounts (again as few as 1 molecule). Theadvantages of the method of the invention are based on the homogeneousnature and their ability to combine equilibrium and non-equilibriumconditions in a single CE run. The three applications of this inventioncan be used for discovery and characterization of drug candidates andthe development of new diagnostic tools.

Application 1. Determination of K_(d) and K_(off) of Complex Formationfrom a Single NECEEM Electropherogram

In one embodiment of this invention, the equilibrium mixture ofmolecules T and L (for which K_(d) and k_(off) are to be determined) isprepared by mixing T and L outside or inside the capillary and allowingthem to reach equilibrium (see equation 1 above). The equilibriummixture can be prepared inside the capillary by, for example,introducing a plug of the component with lower electrophoretic mobilityfirst, and the component with greater electrophoretic mobility second.The components are mixed by applying voltage to the capillary. If theequilibrium mixture is prepared outside the capillary, a plug of theequilibrium mixture is injected into the capillary, preferably bypressure (injection by voltage can disturb the equilibrium). Theequilibrium mixture contains three components: free L, free T, and theL•T complex. The equilibrium mixture is subjected to electrophoresisusing a run buffer that does not contain L or T or L•T. The conditionsfor electrophoresis are optimized (by finding the appropriate run bufferor modifying the surface of inner capillary walls or other means) sothat L and T have different mobilities. The complex will typically havean intermediate mobility. Thus, the equilibrium fraction of at least oneof L or T is removed from the electrophoretic zone of the L•T complex assoon as electrophoresis starts. The equilibrium fractions of L and Tmigrate as single electrophoretic zones and result in two peaks. Theequilibrium fraction of the L•T complex cannot generate a singleelectrophoretic peak since the equilibrium of the complex is notmaintained in NECEEM. The complex continuously decays during theseparation resulting in the non-equilibrium production of free L andfree T. According to equation 1, the rate of L and T production reducesexponentially following the monomolecular decay of the complex duringNECEEM separation:

$\begin{matrix}{\frac{\mathbb{d}\lbrack L\rbrack}{\mathbb{d}t} = {\frac{\mathbb{d}\lbrack T\rbrack}{\mathbb{d}t} = {{- \frac{\mathbb{d}\left\lbrack {L \cdot T} \right\rbrack}{\mathbb{d}t}} = {\left\lbrack {L \cdot T} \right\rbrack_{eq}{\exp\left( {{- k_{off}}t} \right)}}}}} & (3)\end{matrix}$Here [L•T]_(eq) is the equilibrium concentration of the complex in theequilibrium mixture and t is the time from the beginning of separation.In general, the monomolecular decay, represented by equation 3, producestwo exponential curves in the electropherogram (FIG. 1). Finally,complex, that remains intact at the time it passes the detector,generates another peak.

To represent true concentrations of the species, signal intensities andareas in electropherograms must be properly normalized. The approachesof normalization are well known to a person of ordinary skills in theart of CE. Briefly, if absorption detection is used then the areas arenormalized by the extinction coefficients of L and T at the wavelengthor wavelengths of detection. If fluorescence detection is used, then theareas are normalized by quantum yields of L and T. If on-columndetection is used then, the areas must be normalized by the migrationvelocities as well. In the case of past-column sheath flow detection, nonormalization of migration velocities is required since all componentspass the detector with the same velocity defined by the sheath-flowvelocity. In this application it is assumed that the intensities and theareas in the electropherograms are properly normalized.

Depending on whether one or both of L and T are detectable, twosituations may occur.

The first situation is presented in FIG. 1. This figure schematicallyillustrates the important features of a NECEEM electropherogram whenboth L and T are detectable (e.g. diode array detector is used).Depending on the values of k_(off) and the migration time, t_(L•T), ofthe L•T complex, the complex decays to different degrees during itsmigration through the capillary.

If k_(off)<<1/t_(L•T) then no detectable decay will be observed and, ingeneral, the electropherograms will be comprised of three peakscorresponding to L, T, and L•T (FIG. 1A). Since no complex decay isobserved, NECEEM converges into an ordinary equilibrium CE of complexes,which is described in detail in prior art articles. The areas correspondto equilibrium concentrations of L, T, and L•T: [L]_(N), [T]_(eq), and[L•T]_(eq). The value of K_(d) can be found as:

$\begin{matrix}{K_{d} = {\frac{{\lbrack L\rbrack_{eq}\lbrack T\rbrack}_{eq}}{\left\lbrack {L \cdot T} \right\rbrack_{eq}} = \frac{A_{L}A_{T}}{A_{L \cdot T}}}} & (4)\end{matrix}$where A_(T), A_(L), and A_(L•T) are the areas of the peaks correspondingto T, L, and L•T, respectively. To measure k_(off), the conditions(buffer, capillary length, capillary coating, pressure, etc.) of CE mustbe changed to increase t_(L•T) in order to operate under the conditionsof NECEEM.

If k_(off) and 1/t_(L•T) are of the same order of magnitude, thencomplex decay is considerable but the peak corresponding to intact L•Tis still detectable. These are the conditions of NECEEM. The NECEEMelectropherogram in such a case consists of 3 peaks and two decay areas(FIG. 1B). The value of K_(d) can be found from a single NECEEMelectropherogram as:

$\begin{matrix}{K_{d} = {\frac{{\lbrack L\rbrack_{eq}\lbrack T\rbrack}_{eq}}{\left\lbrack {L \cdot T} \right\rbrack_{eq}} = \frac{A_{L}A_{T}}{A_{L \cdot T} + A_{decay}}}} & (5)\end{matrix}$where the equilibrium concentration of the complex [L•T]_(eq) isrepresented by the sum of the two areas, A_(L•T) and A_(decay). The twodecay areas in FIG. 1B are identical since they represent a singleprocess of decay. Only one area is included in equation 5. The value ofk_(off) is found by analyzing the decay data. Three approaches aresuggested here.

In the first approach, a decay line, which defines one of the decayareas, is fitted with a single-exponential function and k_(off) isobtained from this fitting:

$\begin{matrix}{I_{t^{L}} = {I_{t_{0}^{L}}\exp\left\{ {k_{off}\frac{t_{L \cdot T}}{t_{L} - t_{L \cdot T}}\left( {t^{L} - t_{0}^{L}} \right)} \right\}}} & (6)\end{matrix}$for the decay followed by the production of L or

$\begin{matrix}{I_{t^{T}} = {I_{t_{0}^{T}}\exp\left\{ {k_{off}\frac{t_{L \cdot T}}{t_{T} - t_{L \cdot T}}\left( {t^{T} - t_{0}^{T}} \right)} \right\}}} & (7)\end{matrix}$for the decay followed by production of T. In the two last equations thefollowing notations are used: I_(t) _(L) and I_(t) _(T) are the signalintensities at time t corresponding to L and T, respectively; I_(t) _(L)₀ and I_(t) _(T) ₀ are initial signal intensities at times t^(L) ₀ andt^(T) ₀, respectively; t_(L), t_(T), and t_(L•T) are migrations times ofL, T, and L•T, respectively.

In the second approach, k_(off) can be found from the same lines byusing one of the following 2 equations:

$\begin{matrix}{k_{off} = \frac{\ln\left( {I_{t^{L}}/I_{t_{0}^{L}}} \right)}{{t_{L \cdot T}\left( {t_{L}^{L} - t_{0}^{L}} \right)}/\left( {t_{L} - t_{L \cdot T}} \right)}} & (8) \\{or} & \; \\{k_{off} = \frac{\ln\left( {I_{t^{T}}/I_{t_{0}^{T}}} \right)}{{t_{L \cdot T}\left( {t^{T} - t_{0}^{T}} \right)}/\left( {t_{T} - t_{L \cdot T}} \right)}} & (9)\end{matrix}$where t^(L) and t^(T) are fixed time points on the two lines. Formulas 8and 9 were obtained by taking the natural log(ln) function of equations6 and 7.

In the third approach, if the L•T peak is detectable, then k_(off) canbe found by analyzing only the areas:

$\begin{matrix}{k_{off} = \frac{\ln\left( {\left( {A_{L \cdot T} + A_{decay}} \right)/A_{L \cdot T}} \right)}{t_{L \cdot T}}} & (10)\end{matrix}$The last approach is especially useful when the exponential line is“contaminated” so that fitting is problematic. The three describedapproaches can be modified in a number of ways by a person skilled inthe art of CE.

If k_(off)>>1/t_(L•T), then the complex decays to undetectable levelsduring its migration through the capillary. No peak corresponding to L•Tis observed. The electropherogram in such a case consists of 2 peaks andtwo decay areas (FIG. 1C). The value of K_(d) can be found as:

$\begin{matrix}{K_{d} = {\frac{{\lbrack L\rbrack_{eq}\lbrack T\rbrack}_{eq}}{\left\lbrack {L \cdot T} \right\rbrack_{eq}} = \frac{A_{L}A_{T}}{A_{decay}}}} & (11)\end{matrix}$where the equilibrium concentration of the complex [L•T]_(eq) isrepresented by a single area of complex decay, A_(decay). The value ofk_(off) is found by analyzing the decay data and using one of equations6-9. Since the L•T peak is not detectable under these conditions,information on the value of t_(L•T) cannot be obtained using NECEEM. TheNECEEM conditions (separation buffer, capillary coating, pressure)should be changed to shorten the separation time. Alternatively, ACE canbe used by a person of ordinary skills in CE to obtain the value oft_(L•T) (Berezovski and Krylov, Anal. Chem. 2003, 72, 1982).

The second situation is illustrated by FIG. 2. This figure schematicallyshows the important features of a NECEEM electropherogram where only Lis detectable (e.g. a fluorescence detector is used and only L has afluorescence label). A similar approach is applicable to the case whenonly T is detectable. If only L is detectable, then the peak of T willnot be present in the electropherograms. Depending on the values ofk_(off) and the migration time, t_(L•T), of the L•T complex, the complexdecays to different degrees during its migration through the capillary.

If k_(off)<<1/t_(L•T), then no detectable decay of L•T is observed.Since no complex decay is observed, NECEEM converges into an ordinaryequilibrium CE of complexes, which is described in detail in prior artarticles. The CE electropherogram in this case is comprised of two peakscorresponding to L, and L•T (FIG. 2). The areas under the peakscorrespond to equilibrium concentrations of L and L•T: [L]_(eq) and[L•T]_(eq), respectively. Thus, a ratio of the two concentrations can beexperimentally found:

$\begin{matrix}{R = {\frac{\lbrack L\rbrack_{eq}}{\left\lbrack {L \cdot T} \right\rbrack_{eq}} = \frac{A_{L}}{A_{L \cdot T}}}} & (12)\end{matrix}$and the value of K_(d) can be calculated according to the followingequation (for the derivation see supplementary material to Berezovskiand Krylov, Analyst 2003, 128, 571):

$\begin{matrix}{K_{d} = \frac{{\lbrack T\rbrack_{0}\left( {1 + R} \right)} - \lbrack L\rbrack_{0}}{1 + {1/R}}} & (13)\end{matrix}$where [T]₀ and [L]₀ are total concentrations of T and L in theequilibrium mixture. To measure k_(off), the NECEEM conditions(separation buffer, capillary length, capillary coating, pressure, etc.)must be changed to increase t_(L•T).

If k_(off) and 1/t_(L•T) are of the same order of magnitude, thencomplex decay is considerable but the peak corresponding to the intactL•T is still detectable. These are the conditions of NECEEM. The NECEEMelectropherogram in such a case consists of 2 peaks and one decay area(FIG. 2B). The value of K_(d) can be found using equation 13 and thefollowing formula for the equilibrium ratio between the concentrationsof L and L•T:

$\begin{matrix}{R = {\frac{\lbrack L\rbrack_{eq}}{\left\lbrack {L \cdot T} \right\rbrack_{eq}} = \frac{A_{L}}{A_{L \cdot T} + A_{decay}}}} & (14)\end{matrix}$where the equilibrium concentration of complex [L•T]_(eq) is representedby the sum of two areas, A_(L•T) and A_(decay). The value of k_(off) canbe found by analyzing the decay data. The approaches described above andformulas 6-10 can be used to find k_(off).

If k_(off)>>1/t_(L•T), then the complex decays to undetectable levelsduring its migration through the capillary. No peak corresponding to L•Tis observed. The electropherogram in such a case consists of 1 peak and1 decay area (FIG. 2C). The value of K_(d) can be found using equation13 and the following formula for R:

$\begin{matrix}{R = {\frac{\lbrack L\rbrack_{eq}}{\left\lbrack {L \cdot T} \right\rbrack_{eq}} = \frac{A_{L}}{A_{decay}}}} & (15)\end{matrix}$where the equilibrium concentration of the complex [L•T]_(eq) isrepresented by a single decay area, A_(decay). The value of k_(off) isfound by analyzing the decay data and by using one of equations 6-9.Since the L•T peak is not detectable in this case, the information onthe value of t_(L•T) cannot be obtained from NECEEM under theseconditions. The NECEEM conditions (separation buffer, capillary coating,pressure etc.) should be changed to shorten the separation time.Alternatively, ACE can be used by a person of ordinary skills in CE toobtain the value of t_(L•T).

The value of K_(d) is associated with equilibrium mixture conditions,thus it is determined by the incubation buffer, in which the equilibriummixture is prepared. The value of k_(off) is associated with separationconditions, thus it is determined by the electrophoresis run buffer, inwhich complex decay is monitored. If the incubation and run buffers arethe same then, the value of k_(on) can be calculated using the followingequation:k _(on) =k _(off) /K _(d)  (2a)

The method of this invention can be used to determine thermodynamicparameters of reaction 1 if a series of NECEEM procedures are performedat different temperatures. The rate constants and the equilibriumconstant are temperature dependent:

$\begin{matrix}{k_{on} = {A_{on}{\exp\left( {{- E_{a{({on})}}}/{RT}} \right)}}} & (16) \\{k_{off} = {A_{off}{\exp\left( {{- E_{a{({off})}}}/{RT}} \right)}}} & (17) \\{K_{d} = {\exp\left( {{\frac{\Delta\; H^{{^\circ}}}{R}\frac{1}{T}} - \frac{\Delta\; S^{{^\circ}}}{R}} \right)}} & (18)\end{matrix}$where A_(on) and A_(off) are pre-exponential factors for the forward andreverse reactions of equilibrium 1, respectively; E_(a(on)) andE_(a(off)) are activation energies for the forward and reverse reactionsin equilibrium 1, respectively; ΔH° is the reaction enthalpy for process1; ΔS° is the change of entropy in process 1; R is the gas constant andT is the temperature in Kelvin (Note “R” in equations 12-15 is the ratioof equilibrium concentrations, while “R” in equations 16-18 is the gasconstant).

If the equilibrium mixture at different temperatures is analyzed byNECEEM, then K_(d) can be found as a function of temperature, and ΔH°and ΔS° can be determined using equation 18. Similarly, E_(a(on)) andE_(a(off)) can be found using equations 2, 16, and 18 if both K_(d) andk_(off) are measured as functions of temperature.

One embodiment of the method of the invention provides an indirect wayof determining temperature in a capillary or in a channel of achip-based microseparation system by measuring either K_(d) or k_(off).A calibration curve K_(d) vs. T (or k_(off) vs. T) is built using a CEinstrument with a reliable temperature control or SPR. Then, K_(d) (ork_(off)) is measured using a CE apparatus or a chip-based system forwhich the temperature is to be determined. The temperature is determinedfrom the calibration curve by finding the temperature which correspondsto K_(d) (or k_(off)) measured with the instrument in question.Alternatively, the following formula can be used instead of thecalibration curve:

$\begin{matrix}{T = \frac{\Delta\; H^{{^\circ}}}{R\left( {{\Delta\; S^{{^\circ}}R} - {\ln\; K_{d}}} \right)}} & \left( {18a} \right)\end{matrix}$

The method of the invention further provides a unique way for the directmeasurement of fluorescence anisotropy of the L•T complex when L isfluorescently tagged. Traditionally, fluorescence anisotropy of an L•Tcomplex is determined from data obtained in a series of anisotropymeasurements where the concentration of T in the equilibrium mixture isincreased. The equilibrium mixture also contains free L and L•T. Toensure that the majority of L is bound to T, the concentration of T hasto be much higher than the K_(d) of the complex. This constitutes themajor disadvantage of traditional methods. High concentrations of T mayinterfere with fluorescence measurements. Moreover, if T is a protein,high concentrations of T may be difficult to achieve due to solubilityproblems or due to the cost of using expensive proteins. In one methodof the invention, the L•T complex is separated from both the equilibriumfraction of free L and from free L formed during the decay of thecomplex. Thus, the Loa peak is not “contaminated” with free L andfluorescence anisotropy of the peak corresponds to true fluorescenceanisotropy of L•T.

The method of this invention is applicable to finding binding parametersof components of different nature and origin. For example, a componentcan be an organic molecule, protein, peptide, enzyme, nucleic acid,carbohydrate, aptamer, organelle, cell, virus, particle, or otherreagent separable by capillary electrophoresis. If necessary, thecomponent may be pretreated using different procedures such as, but notlimited to: purification, enrichment, fractionation, lysis, freeze-thaw,or centrifugation. The components can be detected using their lightabsorption, fluorescence, electrochemical properties, radioactivity, andmass or charge properties. If the component is not detectable it can belabeled with a tag that facilitates one of the listed above modes ofdetection. The electrophoresis parameters are optimized to facilitateseparation of the components from the complex. This optimization caninclude modifications to the voltage, temperature, buffer composition(including separation-enhancing mediators), buffer pH, capillary lengthor width, or capillary pretreatments such as siliconization or coveringwith dynamic coatings.

The method of this invention in its first application has extremely highsensitivity. If L is fluorescent, and laser-induced fluorescence isused, then as few as 10⁻¹⁸ moles of T are sufficient to determine theK_(d) and k_(off) values of its interaction with L. The values of K_(d)and k_(off) are determined from the analysis of areas in theelectropherogram. The value of k_(off) can also be determined by fittingthe exponential part of the electropherogram with a single-exponentialfunction. Further the method allows for only one component, L or T, tobe detectable. In such a case the method requires that the detectablecomponent be electrophoretically separated from the complex. The methodcan also be applied to complexes which decay to undetectable levels bythe time they reach the detector. If a series of experiments isperformed at different temperatures then a number of thermodynamicparameters (activation energies of forward and reverse reactions (seereaction 1), the reaction enthalpy, and the change of entropy) can bedetermined.

Application 2. Quantitative Analysis of T Using an Affinity Probe L

Another embodiment of the invention is a NECEEM-based method forquantitative affinity analyses of a target molecule, T, using anaffinity probe, L. Affinity probes, in general, are molecules that canbind a target with high specificity and with high affinity. Affinityprobes are typically tagged with a label (radioactive, fluorescent,enzymatic, etc.) that permits detection of both L and L•T. One widelyused example of an affinity probe is antibodies. Another example, whichis still relatively new, is oligonucleotide or peptide aptamers (Clarkand Remcho, Electrophoresis 2002, 23, 1335; WO 0340168; Levy andEllington, Biotechnol. Bioengineer. 2003, 82, 38).

NECEEM of such target-probe pairs generates, in general,electropherograms with two peaks and one exponential curve (see FIGS. 2Band 2C). One peak corresponds to the equilibrium part of the probe,while the second peak corresponds to the non-decayed complex thatreaches the detector. The second peak may not be observed if the complexdecays to undetectable levels during separation. The exponential partrepresents free probe produced during the decay of the complex. Thisapplication of the method of the invention can be realized by twoapproaches.

CE has been used for quantitative affinity analyses using labeledaffinity probes. If k_(off) is low compared to the reciprocal migrationtime (t_(m)) of the complex, k_(off)<<1/t_(m), then the complexundergoes no considerable decay during the separation and NECEEMconverges into an ordinary equilibrium CE. The unknown concentration ofT in the sample can be calculated by determining the areas of the peakscorresponding to L and L•T. If k_(off)≧1/t_(L•T), the complex undergoesdecay during the separation, which results in a decreased area for thepeak corresponding to L•T. If k_(off)>>1/t_(L•T), the L•T peak may beabsent due to decay of the complex to undetectable levels. Thus, ifk_(off)≧1/t_(L•T), then traditional equilibrium CE analyses, which relyon measurements of peaks L and L•T only, either lead to underestimatedvalues for unknown T or become completely impossible. This inventionprovides a NECEEM-based approach that overcomes these problems andfacilitates the use of affinity probes with k_(off)≧1/t_(L•T) forquantitative affinity analyses by CE.

An equilibrium mixture is prepared for molecules T and L, where T is thetarget whose concentration is to be measured and L is the detectableaffinity probe that binds the target according to equation 1. Theequilibrium mixture can be prepared inside or outside the capillary. Itcan be made inside the capillary by, for example, introducing a plug ofthe component with lower electrophoretic mobility first, and thecomponent with greater electrophoretic mobility second. The componentsare mixed by applying voltage to the capillary. If the equilibriummixture is prepared outside the capillary, a plug of the equilibriummixture is injected into the capillary, preferably by pressure(injection by voltage can disturb the equilibrium). The equilibriummixture contains three components: free L, free T and the L•T complexwith only L and L•T being detectable. The equilibrium mixture issubjected to electrophoresis under non-equilibrium conditions. Theconditions for electrophoresis are optimized so that L and L•T havedifferent mobilities. This optimization can include modifications to thevoltage, temperature, buffer composition (including separation-enhancingmediators), buffer pH, capillary length or width, or capillarypretreatment such as siliconization or covering with dynamic coatings.When L leaves the electrophoretic zone of L•T, equilibrium 1 is nolonger maintained. If k_(off)≧1/t_(L•T), the complex undergoes decayduring the separation. Depending on the extent of the decay, one of twotypes of NECEEM electropherograms, depicted in FIGS. 2B and 2C, isobserved.

Two approaches can be used to determine the unknown concentrations of T.The first approach requires that the K_(d) of complex formation bedetermined for the interaction of T and L first, using NECEEM asdescribed above. The unknown concentration of T in the sample can thenbe determined by finding the areas of the three (or two) features in thesingle electropherogram, and by using a simple mathematical formula thatincludes the areas, the concentration of the probe, and the value ofK_(d):[T] ₀ =K _(d) /R+[L] ₀/(1+R)  (19)where [L]₀ is the total concentration of the probe in the sample, R isdetermined from equations 14 or 15 depending on whether or not theelectropherogram obtained exhibits a peak corresponding to L•T. Thisapproach has no restriction on [L]₀ and, thus, is universal.

The second approach requires that a calibration curve be built for thesignal (the ratio, R, of the areas) as a function of the targetconcentration. For finding the unknown concentration of T, the areas ofthe three (or two) features in a single electropherogram are determined,the ratio is calculated and the calibration curve,A_(L)(A_(L•T)+A_(decay)) vs. [T], is used to find the unknownconcentration of the target that corresponds to the same ratio, R, ofthe areas. The “calibration curve” approach requires that the sameconcentration of L be used for building the calibration curve and forexperiments to determine the unknown concentrations of T. The “K_(d)”approach is more universal since different concentrations of L can beused for finding K_(d) and for finding the unknown concentration of thetarget.

The method of the invention allows T to be a wide variety of entitiesincluding, but not limited to: an organic molecule, protein, peptide,enzyme, nucleic acid, aptamer, organelle, cell, virus, particle, orother reagent separable by capillary electrophoresis. L can be anychemical entity than binds the target with required specificity andaffinity. If necessary, T may be pretreated using different proceduressuch as, but not limited to: purification, enrichment, fractionation,lysis, freeze-thaw, and centrifugation. L can be detected using lightabsorption, fluorescence, electrochemical properties, radioactivity,mass or charge properties. If L is not detectable, it can be labeledwith a tag that facilitates one of the above listed modes of detection.

This method can be used as a diagnostic tool to measure theconcentration of T present in a patient or biological sample. The methodof the invention in its second application will be applicable to a widevariety of target-probe pairs that cannot be analyzed with classicalmethods, and which are based on monitoring peaks of L and L•T only, dueto the instability of the target-probe complexes. The NECEEM-basedmethod is superior to ACE-based methods as well because it does notrequire that the target of interest be a separation buffer component.Along with avoiding target influence on electroosmotic flow it alsoallows the analysis of extremely small amounts of target. When the probeis fluorescently labeled this application of the invention canquantitate as few as 1000 molecules of T.

Application 3. Selecting Ligands (L) Capable of Binding a Target (T)with Specified k_(n), k_(off), and K_(d)

The method of the invention in its third application presents a new andpowerful approach to select ligands from complex mixtures. Uniquecapabilities of this method include, but are not limited by: (a) theselection of ligands with specified ranges of k_(on), k_(off), and K_(d)of target-ligand interactions, (b) the selection of ligands present inminute amounts in complex mixtures of biological or synthetic samples,and (c) the selection of ligands for targets available in very lowamounts. The conditions for NECEEM-based screening are chosen such thatthe components of the sample have similar electrophoretic mobilities andthe target has a mobility considerably different from the samplecomponents. Complexes of the target and ligands, which are present inthe sample, will have intermediate mobility that can be estimated if themobilities of the ligands and the target are known. Under suchconditions, the sample migrates as a single electrophoretic zone or as aset of close zones and generates a single peak or a set of close peaks.This peak(s) is distinct from the peak of the target. For the simplicityof presentation, hereafter it is assumed that the sample migrates as asingle electrophoretic peak (see Example 15).

In one embodiment, the method of the invention allows for the collectingof a fraction of ligands, capable of binding to the target with rangesof K_(d) and k_(on), which are defined by the operator, in the followingprocedure:

1. The ligands are selected with the required upper limit of K_(d) andlower limit of k_(on). To facilitate this, the mixture of the target (T)and the sample with potential ligands is prepared and equilibratedinside or outside the capillary. If it is prepared outside thecapillary, a plug of the mixture is introduced into the capillary. Theconcentration of the target, [T]₁, and the time of mixtureequilibration, t_(eq1), are chosen to facilitate the selection ofligands with the required upper limit of K_(d) and lower limit ofk_(on). The upper limit of K_(d) will be equal to [T]₁ while the lowerlimit of k_(on) will be equal to 1/[T]₁t_(eq1). The ligands withK_(d)<[T]₁ and k_(on)>[T]₁t_(eq1) will be preferably bound to T, whileligands with K_(d)>[T]₁ or k_(on)<1/[T]₁t_(eq1) will be preferably in anon-bound state. The mixture is subjected to NECEEM, as described aboveand the sample is monitored if possible. To this end the components ofthe sample can be labeled with a tag facilitating detection. Forexample, if the sample is a combinatorial library of oligonucleotides,all the components can be fluorescently labeled (Example 15). If thetarget is not detectable by NECEEM, the electropherogram consists of asingle peak corresponding to the sample. The target itself may not bedetectable either due to its low concentration or due to the lack of afluorescent (or other) tag. Peaks corresponding to the intact L•Tcomplex and the exponential curve corresponding to its decay, may not bedetectable because the concentration of the ligands in the sample may bebelow the limit of detection. In another embodiment, if the migrationtime of T is not known, then the ligands within L•T, or formed from thedecay of L•T are collected from both sides of peak L (FIG. 3). If themigration time of T is known, then the ligands within L•T, or formedfrom the decay of L•T are collected in the time window t_(T)-t_(L) (ort_(L)-t_(T)) from one side of peak L only (FIG. 4). The pool of ligandscollected in this way contains selectively the ligands with K_(d)<[T]₁and k_(on)>1/[T]₁t_(eq1). The population of ligands with K_(d)<[T]₁ andk_(on)>1/[T]₁t_(eq1) can be enriched if the fraction collected issubjected to another selection using the same procedure. If the amountof these ligands is not sufficient for further selection, the selectionprocedure described above can be repeated as many times as required toaccumulate the required amount of ligands from the sample. If theligands are nucleic acids (e.g. oligonucleotide aptamers), they can beamplified in a PCR procedure, instead. The PCR procedure will enrich thepopulation of ligands with K_(d)<[T]₁ and k_(on)>[T]₁t_(eq1) (seeexample 15).

2. The ligands with K_(d)<[T]₁ and k_(on)>1/[T]₁t_(eq1), that have beenselected as described in the previous paragraph, are screened to furtherselect ligands with [T]₂<K_(d)<[T]₁ and1/[T]₂t_(eq2)>k_(on)>1/[T]₁t_(eq1). To facilitate this, the fractioncontaining ligands selected in the first round and T, are combined andequilibrated. The concentration of the target, [T]₂, and the time ofmixture equilibration, t_(eq2), are chosen to facilitate the selectionof ligands with the required lower limit of K_(d) and upper limit ofk_(on). The lower limit of K_(d) will be equal to [T]₂ while the upperlimit of k_(on) will be equal to 1/[T]₂t_(eq2) where [T]₂<[T]₁ andt_(eq2)<t_(eq1). The ligands with K_(d)<[T]₂ and k_(on)>1/[T]₂t_(eq2)will be preferably bound to T, while ligands with K_(d)>[T]₂ ork_(on)<1/[T]₂t_(eq2) will be preferably in a non-bound state. Themixture is subjected to NECEEM and the fraction that corresponds to freeligands is collected. Depending on: (i) how different [T]₂ is from [T]₁and t_(eq2) is from t_(eq1), and (ii) the total concentration of theligands in the mixture, different types of NECEEM electropherograms willbe observed. First, if [T]₂ is close to [T]₁ and t_(eq2) is close tot_(eq1), then most of the ligands in the mixture will be bound to T andthe peak of free L will not be observed; instead the peak of L•T and thecurve corresponding to the decay of L•T will be observed (FIG. 5A). Incontrast, if [T]₂<<[T]₁ or t_(eq2)<<t_(eq1), then most of the ligandswill be in the non-bound state and a single peak of L will be observed(FIG. 5B). There may be a situation when all three features, two peaksand the decay curve, are detectable (FIG. 5C). In any case, the fractionto be collected corresponds to the time window where the peak L is, orwould be if it were detectable (see FIGS. 5A, 5B and 5C). The range ofK_(d) and k_(on) values of the selected pool of ligands will narrow as[T]₂ approaches [T]₁ and t_(eq2) approaches t_(eq1). To enrich for thepopulation of ligands with [T]₂<K_(d)<[T]₁ and1/[T]₂t_(eq2)>k_(on)>1/[T]₁t_(eq1) in the pool, the selected ligands aresubjected to repetitive procedures of selection. If the amount ofcollected ligands is not sufficient for further work the procedure canbe repeated to accumulate ligands from the sample. If the ligands arenucleic acids (e.g. oligonucleotide aptamers), they can be amplified ina PCR procedure. The values of K_(d), k_(on), and k_(off) areinterconnected through equation 2. Therefore, ligands with[T]₂<K_(d)<[T]₁ and 1/[T]₂t_(eq2)>k_(on)>1/[T]₁t_(eq1) have a definedrange of k_(off): [T]₁/[T]₂t_(eq2)>k_(off)>[T]₂/[T]₁t_(eq1). There is anatural limitation for the upper limit of k_(on); the upper limit ofk_(on) cannot exceed the diffusion controlled rate constant, which istypically less than 10¹° M⁻¹s⁻¹.

In another embodiment, the method of the invention advantageously allowsfor the collection of ligands, capable of binding to the target within arange of k_(off) values as defined by the operator. The mixture of thetarget and sample, or a pre-selected pool of ligands, is prepared withthe concentration of the target that permits binding of most of theligands. It is advantageous to chose a concentration of T higher than[T]₁. The information provided by the decaying complex can bemanipulated by a person skilled in the art of CE in several ways, two ofwhich are presented here:

1. It is possible to select the most stable complexes withk_(off)<k_(off) ^(max). This can be done by adjusting the migration timeof the complex, t_(L•T), so that t_(L•T)=1/k_(off) ^(max) and collectingthe fraction L•T (FIG. 6A). The value of t_(L•T) can be adjusted bychanging the NECEEM separation conditions (within the knowledge of oneskilled in the art of CE) such as the length of the capillary, voltage,the composition and pH of the run buffer, etc. If the peak of L•T is notdetectable then a fraction is collected blindly in the time window wherethe peak would be observed if the amount of intact L•T were detectable.If the amount of collected ligands is not sufficient for further work,the procedure can be repeated to accumulate ligands. If the ligands arenucleic acids (e.g. oligonucleotide aptamers), they can be amplified ina PCR procedure.

2. If ligands with k_(off) ^(min)<k_(off)<k_(off) ^(max) are required,they can be selected by collecting fractions of the decaying complex(FIG. 6B). It is essential in this case to exclude the L•T peak since itcontains a pool of ligands with no lower limit of k_(off). The rate ofproduction of L as the complex decays, is described in equation 3. Thequestion to be answered is what is the value of k_(off) of the ligandsthat are preferably selected if a fraction is collected at time t fromthe beginning of separation? To answer this question k_(off) has to befound, for which the rate of L formation is maximal at time t. To findthis, the following equation has to be solved:

$\begin{matrix}{{{\frac{\mathbb{d}}{\mathbb{d}k_{off}}\frac{\mathbb{d}\lbrack L\rbrack}{\mathbb{d}t}} = 0}\begin{matrix}{{\frac{\mathbb{d}}{\mathbb{d}k_{off}}\frac{\mathbb{d}\lbrack L\rbrack}{\mathbb{d}t}} = {\frac{\mathbb{d}}{\mathbb{d}k_{off}}\left\{ {\left\lbrack {L \cdot T} \right\rbrack_{eq}k_{off}{\exp\left( {{- k_{off}}t} \right)}} \right\}}} \\{= {{\left\lbrack {L \cdot T} \right\rbrack_{eq}{\exp\left( {{- k_{off}}t} \right)}} - {k_{off}{t\left\lbrack {L \cdot T} \right\rbrack}_{eq}{\exp\left( {{- k_{off}}t} \right)}}}} \\{= {\left\lbrack {L \cdot T} \right\rbrack_{eq}{\exp\left( {{- k_{off}}t} \right)}\left( {1 - {k_{off}t}} \right)}} \\{= 0}\end{matrix}} & (20)\end{matrix}$This equation has one solution:K _(off)=1/tIf the fraction is collected in the time window between t₁ and t₂ (seeFIG. 6B), then ligands with 1/t₂<k_(off)<1/t₁ are selected preferably.Because

$\frac{\mathbb{d}}{\mathbb{d}k_{off}}\frac{\mathbb{d}\lbrack L\rbrack}{\mathbb{d}t}$is a smooth function of k_(off), ligands with k_(off)>1/t₁ andk_(off)<1/t₂ may also be present in the fraction collected between t₁and t₂ even though their selection is less efficient than that ofligands with 1/t₂<k_(off)<1/t₁. The ligand population with desirable1/t₂<k_(off)<1/t₁ can be enriched if the fraction collected is subjectedto another NECEEM procedure with fraction collection within the sametime window, t₁-t₂. If the amount of collected ligands is not sufficientfor further work, the procedure of collecting the peak can be repeatedto accumulate ligands. If the ligands are nucleic acids, they can beamplified in a PCR procedure.

When selecting for k_(off), the following natural limitation has to betaken into consideration. The maximum possible k_(on) value is thediffusion controlled one, which does not typically exceed 10¹⁰ M⁻¹s⁻¹.Using equation 2 the upper limit of the decay constant can be expressedas a function of K_(d):k _(off)<10¹⁰ K _(d)  (22)Thus, K_(d) of the ligands defines the upper limit of k_(off). Forexample, if K_(d)=10⁻¹² M, then k_(off)<10⁻² l/s.

In another aspect of the method of the invention, the equilibriummixture is subjected to capillary electrophoresis using a run bufferthat contains the target at concentration [T]_(buf). In this case, theligand-target equilibrium is maintained during the separation. Themigration time of different ligands will depend on the K_(d) values ofcorresponding ligand-target complexes. If the population of ligandscapable of binding the target within the desired K_(d) range,(comparable to [T]_(buf)), is very low, then only the peak correspondingto non-bound components of the sample may be detectable (FIG. 7A). Thedistribution of the migration times is governed by the Scotchard plot(FIG. 7B). This approach allows the selection of ligands with desiredK_(d) values. This method has the highest accuracy and precision withrespect to determining the K_(d) value of collected ligands when thebuffer contains the concentration of the target equal to the value ofthe desired K_(d) and the fraction is collected in the middle of thet_(min)-t_(T) time window (see FIG. 7A).

An embodiment of the method of this invention can be applied to amixture of targets. In this case it facilitates the selection of ligandsto multiple targets. If the complexes of these targets with the ligandscan be separated, the method can be used to collect individualcomplexes. The ligands in such complexes can then be identified usingother analytical procedures such as a chromatography- orelectrophoresis-based affinity analyses. T can be an organic molecule,protein, peptide, enzyme, nucleic acid, aptamer, organelle, cell, virus,particle, or other reagent separable by capillary electrophoresis. L canbe any chemical entity than binds the target with required specificityand affinity. L may be a component of the biological sample, patientsample, combinatorial library or other complex mixture. If necessary, Tand the sample may be pretreated using different procedures such as, butnot limited to: purification, enrichment, fractionation, lysis,freeze-thaw, and centrifugation. Advantageously, the analytical devicecan be coupled with the capillary electrophoresis instrument. If such adevice is a PCR machine, then the procedure for selecting nucleic acidligands can be automated. If such a device is a mass-spectrometer, thenthe structure of the ligands can be identified in an “on-line” mode.

To conclude, the method of this invention in its third applicationadvantageously does not require monitoring the shift of the peak of thetarget. It does not require that the ligands be in detectableamounts—the ligands can be selected “blindly”. Furthermore, the methoddoes not require the presence of detectable amounts of target in theequilibrium mixture. This allows for selecting very tight ligands withvery low values of K_(d) (e.g. K_(d)<10⁻⁹ M). The method facilitatesrepetitive refinement procedures that can lead to a series of ligandswith very narrow ranges of K_(d), k_(on), and k_(off) values or even toa single ligand with desirable K_(d), k_(on), and k_(off) parameters.

Uses

In general, the method of the invention can be used for discovery andcharacterization of drug candidates and the development of newdiagnostic tools.

The method of this invention will be useful for selecting drugcandidates from combinatorial (or other) libraries. Its usefulness isemphasized by its unique ability to select drug candidates withspecified values of binding parameters to the therapeutic target.Furthermore, the method of the invention, when performed at differenttemperatures, will allow the selection of molecules with desirablethermodynamic parameters of binding to the therapeutic target. Thisunique ability of the method is especially important for developingdrugs whose activity is regulated by changing temperatures of the body,such as anti-inflammatory drugs.

The method of the invention will be useful for developing diagnosticprobes. Such probes are also subject to the requirements of specificbinding parameters between probe and target and the specific dependenceof these parameters on temperature. A person with ordinary skills in CEwill be able to use the method for the selection of diagnostic probes ordrug candidates from different types of combinatorial libraries.

Another exciting application of the method is the selection of aptamersfrom combinatorial libraries. In particular, the method of thisinvention is very advantageous for selecting oligonucleotide aptamersfor proteins. Oligonucleotide libraries have a unique electrophoreticmobility since oligonucleotides have identical electrophoreticmobilities, independently of their length or hybridization status.Proteins typically have electrophoretic mobility much greater than thatof oligonucleotide libraries. Therefore, a protein-aptamer complextypically migrates faster than non-bound oligonucleotides. As a result,non-specific interactions of oligonucleotides with capillary walls donot cause background interference in the selection process. This inturn, allows the method to be used for the selection of aptamers forextremely small amounts of targets. In the first use of the method (seeexample 15) an aptamer was selected using an amount of target protein, 5orders of magnitude lower than current state-of-the art methods permitfor selection of aptamers (Vant-Hull et al., J. Mol. Biol., 1998, 278,579).

The method of this invention will be useful for finding bindingparameters between drug candidates (developed using other methods) andtheir therapeutic targets. It will also find use in determiningtemperature inside channels of microfabricated devices.

The method of this invention will be useful for developing diagnostic abased on CE and aptamers. This method can also be used as a diagnostictool for the quantification of parameters modified by disease (i.e.altered levels of metabolic products, presence of viral DNA etc.) inpatient samples. Many heterogeneous diagnostic methods such as ELISAhave unacceptably high levels of false positives due to the limitationsdiscussed above. This invention can provide an alternative to suchmethods that afford a greater degree of accuracy and sensitivity. Sincethe method can detect T present in very low concentrations, it mayprovide enhanced detection of disease markers permitting earlierdiagnosis and enhanced treatment options.

The following non-limiting examples are illustrative of the presentinvention.

EXAMPLES

The following examples are illustrative of preferred embodiments ofmethods of the invention and are not to be considered as limiting theinvention thereto.

Example 1 FIG. 1

Schematic illustration for the determination of K_(d) and k_(off) valuesby NECEEM when both L and T are detectable. Panels A, B, and Ccorrespond to low, intermediate and high k_(off) values, respectively.

Panel A. When k_(off) is low, k_(off)<<1/t_(L•T), then the complex doesnot decay during its migration through the capillary. NECEEM thenconverges into an ordinary equilibrium CE. In an ordinary equilibriumCE, three peaks are observed, corresponding to L, L•T, and T withnormalized areas A_(L), A_(L•T), and A_(T), respectively. The areas ofthe peaks represent the equilibrium fractions of L, L•T, and T. Thevalue of K_(d) can be found using equation 4. In order to determine thevalue of k_(off), the retention time of L•T in the capillary should beincreased to transform the ordinary equilibrium CE into NECEEM. This canbe achieved by changing a number of parameters, such as, but not limitedto: run buffer components, run buffer ionic strength, run buffer pH,electric filed, and capillary length. Panel B. When k_(off) isintermediate, k_(off)˜1/t_(L•T), then the complex experiences adetectable degree of decay during its migration through the capillary.In this case, three peaks are still observed. In addition to the threepeaks there are two decay areas, each of which is referred to asA_(decay), corresponding to the fraction of L•T that decayed during theseparation. The equilibrium fraction of L•T is represented by the sumarea A_(L•T)+A_(decay). The value of K_(d) can be determined usingequation 5. The value of k_(off) can be determined using equations 8-10.

Panel C. When k_(off) is high, k_(off)>>1/t_(L•T), then the complexdecays so that the intact complex is not detectable. Only two peaks andtwo decay areas are observed. The equilibrium fraction of L•T isrepresented by a sole A_(decay) area. The value of K_(d) can bedetermined using equation 11. The value of k_(off) can be determinedusing either of equations 8-9. In order to use equation 10, theretention time of the complex in the capillary must be decreased toallow for detection of the L•T peak. The retention time can be decreasedby changing a number of parameters, such as, but not limited to: runbuffer components, run buffer ionic strength, run buffer pH, electricfiled, and capillary length.

Example 2 FIG. 2

Theoretical illustration for the determination of K_(d) and k_(off)values by NECEEM when only L is detectable. Panels A, B and C correspondto low, intermediate, and high k_(off) values, respectively.

FIG. 2 schematically exemplifies the important features in a NECEEMelectropherogram when only L is detectable (e.g. a fluorescence detectoris used and only L has a fluorescent label). A similar approach isapplicable when only T is detectable. If only L is detectable, the Tpeak is not present in the electropherograms. Depending on the values ofk_(off) and the migration time, t_(L•T), of the L•T complex, the complexdecays to different degrees during its migration through the capillary.

Panel A. If k_(off)<<1/t_(L•T) then no detectable decay is observed.NECEEM then converges into an ordinary equilibrium CE. In ordinaryequilibrium CE, the electropherogram is comprised of two peakscorresponding to L, and L•T with normalized areas A_(L), and A_(L•T),respectively. The areas correspond to equilibrium concentrations of Land L•T, [L]_(eq) and [L•T]_(g), respectively. Thus, a ratio of the twoconcentrations can be experimentally found:

$\begin{matrix}{R = {\frac{\lbrack L\rbrack_{eq}}{\left\lbrack {L \cdot T} \right\rbrack_{eq}} = \frac{A_{L}}{A_{L \cdot T}}}} & (12)\end{matrix}$and the value of K_(d) can be calculated according to the followingequation:

$\begin{matrix}{K_{d} = \frac{{\lbrack T\rbrack_{0}\left( {1 + R} \right)} - \lbrack L\rbrack_{0}}{1 + {1/R}}} & (13)\end{matrix}$where [T]₀ and [L]₀ are total concentrations of T and L in theequilibrium mixture. To measure k_(off), the conditions (separationbuffer, capillary length, capillary coating, pressure, etc.) of NECEEMmust be changed to increase t_(L•T) to transform the ordinaryequilibrium CE into NECEEM.

Panel B. If k_(off) and 1/t_(L•T) are of the same order of magnitude,then complex decay is considerable but the peak corresponding to intactL•T is still detectable. The electropherogram in such a case consists of2 peaks and one decay area. The value of K_(d) can be found usingexpression 13 and the following formula for R:

$\begin{matrix}{R = {\frac{\lbrack L\rbrack_{eq}}{\left\lbrack {L \cdot T} \right\rbrack_{eq}} = \frac{A_{L}}{A_{L \cdot T} + A_{decay}}}} & (14)\end{matrix}$where the equilibrium concentration of the complex [L•T]_(eq) isrepresented by the sum of two areas, A_(L•T) and A_(decay). The value ofk_(off) is found by analyzing the decay data. The approaches describedabove and one of the formulas 6-10 can be used to find k_(off).

Panel C. If k_(off)>>1/t_(L•T), then the complex decays to undetectablelevels during its migration through the capillary. No peak correspondingto L•T is observed. The electropherogram in such a case consists of 1peak and 1 decay area. The value of K_(d) can be found using expression(13) and the following formula for R:

$\begin{matrix}{R = {\frac{\lbrack L\rbrack_{eq}}{\left\lbrack {L \cdot T} \right\rbrack_{eq}} = \frac{A_{L}}{A_{decay}}}} & (15)\end{matrix}$where the equilibrium concentration of the complex [L•T]_(eq) isrepresented by a single decay area, A_(decay). The value of k_(off) isfound by analyzing the decay data and using one of the equations 6-9.Since the L•T peak is not detectable in this case, the information onthe value of t_(L•T) cannot be obtained from NECEEM under theseconditions. The NECEEM conditions (separation buffer, capillary coating,pressure etc.) should be changed to shorten the separation time.Alternatively, ACE can be used by a person of ordinary skills in CE toobtain the value of t_(L•T). The value of K_(d) is associated with theconditions of the equilibrium mixture, and thus is determined by theincubation buffer. The value of k_(off) is associated with theseparation conditions, and thus is determined by the separation buffer.If the incubation and separation buffers are the same, then the value ofk_(on) can be calculated using expression 2.

Example 3 FIG. 3

Theoretical illustration of using a NECEEM-based method for theselection of ligands with K_(d)<K_(d) ^(max)=[T]₁ and k_(on)>k_(on)^(min)=1/[T]₁t_(eq1), when the migration time of the target is unknown.

The ligands are selected with the required upper limit of K_(d) andlower limit of k_(on). To facilitate this, the mixture of T and thesample, which contains potential ligands, is prepared and equilibrated.The concentration of the target, [T]₁, and the time of mixtureequilibration, t_(eq1), are chosen to facilitate the selection ofligands with the required upper limit of K_(d) and lower limit ofk_(on). The upper limit of K_(d) will be equal to [T]₁ while the lowerlimit of k_(on) will be equal to 1/[T]₁t_(eq1). The ligands withK_(d)<[T]₁ and k_(on)>1/[T]₁t_(eq1) will be preferably bound to T, whileligands with K_(d)>[T]₁ or k_(on)<1/[T]_(eq1) will be preferably in anon-bound state. The mixture is subjected to NECEEM, which works asdescribed above but which may generate a new type of electropherogramconsisting of only a single peak. This peak will correspond to thesample components, which do not bind to the target. All the componentsof the sample may be fluorescently tagged but the target itself may notbe detectable either because its concentration is below the limit ofdetection or because only the sample has been labeled. The peakcorresponding to the intact L•T complex and the exponential curvecorresponding to its decay may not be detectable because theconcentration of the ligands in the sample may be below the limit ofdetection. If the migration time of T is not known, then the ligandscomprising L•T or formed from the decay of L•T are collected from bothsides of peak L.

Example 4 FIG. 4

Theoretical illustration of using a NECEEM-based method for theselection of ligands with K_(d)<K_(d) ^(max)=[T]₁ and k_(on)>k_(on)^(min)=1/[T]₁t_(eq1), when the migration time of the target is known.

Ligands are collected between t_(T) and t_(L) from one side of peak Lonly: To the left of peak L, if t_(T)<t_(L) (Panel A) and to the rightof peak L, if t_(T)<t_(L) (Panel B).

Example 5 FIG. 5

Schematic representation of a NECEEM electropherogram during theselection of ligands with K_(d)>K_(d) ^(min) and k_(on)<k_(on) ^(max).

Panel A: [T]₂ and t_(eq2) are slightly less than [T]₁ and t_(eq1),respectively. Most of the ligands in the pool bind to T and are observedeither as peak L•T or its exponential decay. No peak of L is detectable.The fraction of ligands is to be collected in the time window where Lwould be, if it were detectable. The pool of selected ligands will havenarrow ranges of K_(d) (varying from [T]₂ to [T]₁) and k_(on) (varyingfrom t_(eq2) to t_(eq1)).

Panel B: [T]₂<<[T]₁ or t_(eq2)<<t_(eq1). Few of the ligands in the poolbind to T. No peak for L•T or its exponential decay are detectable.Instead, only peak L is observed. Peak L is to be collected. The pool ofselected ligands will have a large range of K_(d) (varying from [T]₂ to[T]₁) or k_(r), (varying from t_(eq2) to t_(eq1)).

Panel C: At least one of [T]₂ and t_(eq2) has an intermediate value. Thesecond parameter, [T]₂ or t_(eq2), cannot be much less than [T]₁ ort_(eq1). A considerable fraction of the ligands bind to T, while asignificant fraction do not bind to T. Peaks L and L•T, as well as theexponential decay of L•T, are detectable. Peak L is collected. The poolof selected ligands will have an intermediate range of K_(d) values(varying from [T]₂ to [T]₁ or k_(on) values (varying from t_(eq2) tot_(eq1)) or both K_(d) and k_(on) values.

Example 6 FIG. 6

Theoretical illustration using a NECEEM-based method for the selectionof ligands with k_(off)<k_(off) ^(max)=1/t₁ and 1/t₂=k_(off)^(min)<k_(off)<k_(off) ^(max)=1/t₁, where t₁ and t₂ are time pointslimiting the time window of fraction selection.

Panel A. To select ligands with k_(off)<k_(off) ^(max), a fraction ofL•T is collected. The migration time of L•T, t_(L•T), is adjusted bychanging the NECEEM conditions to satisfy t_(L•T)=1/k_(off) ^(max).

Panel B. To select ligands with k_(off) ^(min)<k_(off)<k_(off) ^(max), afraction of L originating from the decaying complex is collected. Thetime window of collection, t₁-t₂, is chosen to satisfy: t₁=1/k_(off)^(max) and t₂=1/k_(off) ^(min). The conditions of NECEEM are adjusted toensure that t_(L•T)>t₂.

Example 7 FIG. 7

Schematic representation of an electropherogram during the selection ofligands from a sample with a very low fraction of ligands, using a runbuffer that contains the target at concentration [T]_(buf).

The equilibrium mixture is subjected to capillary electrophoresis usinga run buffer that contains the target at concentration [T]_(buf). Inthis case, the ligand-target equilibrium is maintained during theseparation. The migration time of different ligands will depend on theK_(d) values of corresponding ligand-target complexes. If the populationof ligands capable of binding the target with a K_(d) value comparableto [T]_(buf) is very low, then only the peak corresponding to non-boundcomponents of the sample may be detectable (Panel A). The distributionof the migration times is governed by the Scotchard plot (Panel B). Thisapproach allows selecting ligands with desired K_(d) values. This methodhas the highest accuracy and precision with respect to the K_(d) valueof collected ligands when the buffer contains the concentration of thetarget equal to the value of the desired K_(d) and the fraction iscollected in the middle of the t_(min)-t_(T) time window.

Example 8 FIG. 8

The Determination of Equilibrium and Kinetic Parameters of ComplexFormation Between SSB and ssDNA.

SSB and a fluorescently-labeled 15-mer ssDNA oligonucleotide,5′-fluorescein-GCGGAGCGTGGCAGG (SEQ ID NO: 1) (fDNA) were used in thisexample (Berezovski and Krylov J. Amer. Chem. Soc. 2002, 124, 13674).NECEEM separation of protein-DNA complexes was performed using alaboratory-built CE instrument with fluorescence detector described indetail elsewhere (Wu and Dovichi J. Chromatogr. 1989, 480, 141). A 488nm line of an Argon-ion laser was utilized to excite the fluorescence ofthe DNA. Uncoated fused silica capillaries of 40 cm×20 μm I.D.×150 μmO.D. were used. The electrophoresis was run with a positive electrode atthe injection end biased at +24 kV. The run buffer for NECEEM was 25.0mM tetraborate at pH 9.4. The samples were injected into the capillaryby a pressure pulse of 1 s×9.1 kPa; the length of corresponding sampleplug was 0.93 mm as was calculated using the Poiseulle equation (Krylovet al. Anal. Chem. 2000, 72, 872). The capillary was rinsed with the runbuffer solution for 2 minutes prior to each run. At the end of each run,the capillary was rinsed with 100 mM NaOH for 2 minutes, followed by arinse with deionized water for 2 minutes.

Equilibrium mixtures of SSB, fDNA and SSB•fDNA complex were prepared bymixing solutions of 16 μM SSB and 205 nM fDNA in the run buffer at adesired volume ratio and incubating them at room temperature to reachequilibrium prior to the analysis. Equilibrium mixtures contained threecomponents: free SSB, free fDNA and the fDNA•SSB complex. FIG. 8 showsthat NECEEM separation of such mixtures generated electropherograms withthree essential features: peak 1 (with area A₁) corresponding to freefDNA, peak 2 (with area A₂) corresponding to the ssDNA•SSB complex thatremained intact at the time it passed the detector, and exponentialcurve 3 (with area A₃) corresponding to the decay of fDNA•SSB during theseparation. The areas were determined and the value of K_(d) wascalculated using equation 13, K_(d)=2.8×10⁻⁷ M.

The exponential curve was fitted with a single-exponential function 6and the value of k_(off) was determined, k_(off)=3.3×10⁻² s⁻¹. The valueof k_(on) was then calculated using equation 2, k_(on)=1.2×10⁵ M¹ s⁻¹.

Example 9 FIG. 9

The Determination of Equilibrium and Kinetic Parameters of ComplexFormation Between the Mef2c Protein and dsDNA.

Mef2c DNA-binding protein and its dsDNA target were used in thisexample. The target dsDNA was a total of 26 base pairs including the 10base pair-long sequence, GATTTTTATT (SEQ ID NO: 6), binding site ofMef2c. The dsDNA was labeled with fluorescein. NECEEM separation ofprotein-DNA complexes was performed using a commercial P/ACE MDQapparatus (Beckman-Coulter) with fluorescence detection. A 488 nm lineof an Argon-ion laser was utilized to excite the fluorescence of thedsDNA. Uncoated fused silica capillaries of 40 cm×20 μm I.D.×375 μm O.D.were used. Electrophoresis was carried out with a positive electrode atthe injection end biased at +16 kV. The run buffer used for NECEEM was25.0 mM tetraborate at pH 9.4. The samples were injected into thecapillary by a pressure pulse of 5 s×5 psi; the length of correspondingsample plug was 4 mm as was calculated using the Poiseulle equation(Krylov et al. Anal. Chem. 2000, 72, 872). The capillary was rinsed withthe run buffer solution for 2 minutes prior to each run. At the end ofeach run, the capillary was rinsed with 100 mM NaOH for 2 minutes,followed by a rinse with deionized water for 2 minutes.

Equilibrium mixtures of Mef2c, dsDNA and Mef2c•dsDNA complex wereprepared by mixing Mef2c (1.0 μM) and dsDNA (100 nM) in the run buffer,and incubating them at room temperature to reach equilibrium prior tothe analysis. Equilibrium mixtures contained three components: freeMef2c, free dsDNA and the Mef2c•dsDNA complex. FIG. 9 shows the NECEEMseparation of such mixtures generated electropherograms with threeessential features: peak 1 (with area A₁) corresponding to free dsDNA,peak 2 (with area A₂) corresponding to the Mef2c•dsDNA complex thatremained intact at the time of passing the detector and exponentialcurve 3 (with area A₃) corresponding to the decay of the Mef2c•dsDNAcomplex during separation. The areas were determined and the values ofK_(d) and k_(off) were calculated using equations 13 and 10,respectively: K_(d)=4.8×10⁻⁴ M, k_(off)=0.022 s⁻¹. The value of k_(on)was then calculated using equation 2: k_(on)=45 M⁻¹ s⁻¹. NECEEM allowedthe determination of binding parameters of Mef2c with its dsDNA targetfor the first time.

Example 10 FIG. 10

Determination of Equilibrium and Kinetic Parameters of Complex FormationBetween DNA Polymerase and its Aptamer.

Taq DNA polymerase and its dsDNA aptamer (Yakimovich et al.Biochemistry, Moscow, 2003, 68, 228) were used in this example. Theaptamer was fluorescently-labeled with a 15-mer oligonucleotide,5′-fluorescein-GCGGAGCGTGGCAGG SEQ ID NO: 1) (fDNA). To facilitate thiskind of labeling, the aptamer was extended with a strand of DNAcomplementary to the fDNA. FDNA formed a hybridization complex with theDNA extension on the aptamer. The labeling procedure involved simplymixing the extended aptamer with the fDNA. Since it is impossible toensure an ideal 1:1 ratio between the aptamer and fDNA while mixing, oneof the components is present in excess and can be separated from theother.

NECEEM of protein-DNA complexes was performed using a commercial P/ACEMDQ apparatus (Beckman-Coulter) with fluorescence detection. A 488 nmline of an Argon-ion laser was utilized to excite the fluorescence ofthe labeled aptamer. Uncoated fused silica capillaries of 40 cm×75 μmI.D.×375 μm O.D. were used. Electrophoresis was carried out with apositive electrode at the injection end biased at +16 kV. The run bufferused for NECEEM contained 100 nM SSB in 25.0 mM tetraborate at pH 9.4(SSB in the run buffer was needed to separate the excess of fDNA fromthe aptamer). The samples were injected into the capillary by a pressurepulse of 5 s×0.5 psi; the length of corresponding sample plug was 5 mmas was calculated using the Poiseulle equation (Krylov et al. Anal.Chem. 2000, 72, 872). The capillary was rinsed with the run buffersolution for 2 minutes prior to each run. At the end of each run, thecapillary was rinsed with 100 mM NaOH for 2 minutes, followed by a rinsewith deionized water for 2 minutes.

Equilibrium mixtures of Taq DNA polymerase, its aptamer and the complexof the protein and aptamer, were prepared by mixing solutions of 50 nMTaq DNA polymerase and 100 nM aptamer in the run buffer, at a desiredvolume ratio and incubating them at room temperature to reachequilibrium, prior to the analysis. Equilibrium mixtures contained fourcomponents: free Taq DNA polymerase, free aptamer, the Taq DNApolymerase•aptamer complex and excess fDNA. FIG. 10 shows that NECEEMseparation of such mixtures generated electropherograms with fouressential features: peak 1 (with area A₁) corresponding to free aptamer,peak 2 (with area A₂) corresponding to the Taq DNA polymerase•aptamercomplex that remained intact by the time of its passing the detector andexponential curve 3 (with area A3) corresponding to the decay of the TaqDNA polymerase•aptamer complex during the separation, and excess fDNA.The areas were determined and the values of K_(d) and k_(off) werecalculated: K_(d)=1.35×10⁻⁹ M and k_(off)=0.01 s⁻¹. The value of k_(on)was then calculated using the follow equation, k_(on)=7.4×10⁶ M⁻¹ s⁻¹.

Example 11 FIG. 11

The Use of a DNA-Binding Protein as an Enhancer of Separation of ssDNAfrom dsDNA in the Determination of Equilibrium and Kinetic Parameters ofa DNA Hybridization Complex Formation.

To use NECEEM in studies of binding parameters of DNA hybridizationreactions, ssDNA has to be separated from the dsDNA hybrid.Electrophoretic mobilities of ssDNA and dsDNA are similar in a gel-freeelectrophoresis buffer. Therefore, ssDNA cannot be readily separatedfrom dsDNA in such a media. Using gel in NECEEM may not be practical asit increases the separation time. Here, it is demonstrated that SSB canfacilitate efficient separation of ssDNA from dsDNA in a gel-freebuffer. This tool is used in the NECEEM study of kinetic and equilibriumparameters of DNA hybridization reactions.

NECEEM analyses were performed using a commercial P/ACE MDQ apparatus(Beckman-Coulter) with fluorescence detection. A 488 nm line of anArgon-ion laser was utilized to excite the fluorescence of thefluorescently labeled DNA. Uncoated fused silica capillaries of 40 cm×20μm I.D.×375 μm O.D. were used. The distance from the injection end tothe detector was 30 cm. Electrophoresis was run with a positiveelectrode at the injection end biased at +16 kV (400 V/cm). The runbuffer used for NECEEM was 25.0 mM tetraborate at pH 9.4 supplementedwith 100 nM SSB protein. The samples were injected into the capillary bya pressure pulse of 5 s×5 psi; the length of corresponding sample plugwas 4 mm as was calculated using the Poiseulle equation (Krylov et al.Anal. Chem. 2000, 72, 872). The capillary was rinsed with the run buffersolution for 2 minutes prior to each run. At the end of each run, thecapillary was rinsed with 100 mM NaOH for 2 minutes, followed by a rinsewith deionized water for 2 minutes.

In this example, binding parameters of the hybridization complex weredetermined between two 10 base-pair long complementary strands of thefollowing sequence: GATTTTTATT (SEQ ID NO: 6). To demonstrate the powerof the proposed method a rather complex equilibrium mixture wasdesigned. It was prepared by mixing three solutions: (i) 200 nM5′-fluorescein-GCGGAGCGTGGCAGG (SEQ ID NO: 1) (DNA-1), (ii) 200 nM5′-TTATTTTTAG (SEQ ID NO: 3) (DNA-2), and 100 nM5′-CCTGCCACGCTCCGCTCTAAAAATAA (SEQ ID NO: 2) (DNA-3) and incubating themat room temperature to reach equilibrium prior to analysis. DNA-1 andDNA-2 formed a hybrid with DNA-3 (FIG. 11). The total concentrations ofDNA-1 and DNA-2 were 200 nM while that of DNA-3 was 100 nM. Theequilibrium mixture contained six components: three single stranded DNAmolecules (DNA-1, DNA-2, DNA-3) and three complexes (DNA-1•DNA-3,DNA-2•DNA-3, and DNA-1•DNA-3•DNA-2). Only DNA-1 was fluorescentlylabeled; thus only the following components were detectable: DNA-1,DNA-1•DNA-3, and DNA-1•DNA-3•DNA-2.

When NECEEM was conducted using a run buffer lacking SSB, a single peakwas observed—the components of the equilibrium mixture could not beseparated without SSB. In the SSB-containing run buffer experiment, atypical NECEEM electropherogram was observed (see FIG. 11). Theequilibrium fraction of DNA-1, which was SSB-bound-ssDNA, migratedfaster than all other components. It generated the peak with theshortest migration time. The DNA-1•DNA-3 complex had a 10-base-pair-longoverhang of ssDNA that could also bind SSB. The DNA-1•DNA-3 complexgenerated a shoulder to the peak of DNA-1. DNA-1•DNA-3•DNA-2 was dsDNAwith no single-stranded overhangs; thus it did not bind SSB and migratedmuch slower than DNA-1 and DNA-1•DNA-3. It generated the peak with thelongest migration time. During its separation, DNA-1•DNA-3•DNA-2,experienced decay—DNA-2 was dissociating from DNA-1•DNA-3•DNA-2 andgenerated a typical single-exponential decay trace. The value ofk_(off)=3×10⁻³ s⁻¹ was calculated from the areas using equation 10. Thevalue of K_(d) was found to be 2.7×10⁻⁷ M from equation 13. The value ofk_(on) was then calculated from equation 2 as 1.1×10⁴ M⁻¹ s⁻¹.

Example 12 FIG. 12

Determination of Thermodynamic Parameters of Complex Formation BetweenSSB and a 15-mer Oligonucleotide.

In this example NECEEM was used to determine the activation energy offorward and reverse reactions, reaction enthalpy as well as the changeof entropy. SSB and fDNA were used in this example. NECEEM separation ofSSB•fDNA complexes was performed using a commercial P/ACE MDQ apparatus(Beckman-Coulter) with fluorescence detection. A 488 nm line of anArgon-ion laser was utilized to excite the fluorescence of the fDNA.Uncoated fused silica capillaries of 40 cm×20 μm I.D.×375 μm O.D. wereused. Electrophoresis was carried out with a positive electrode at theinjection end biased at +16 kV. The run buffer for NECEEM was 25.0 mMtetraborate at pH 9.4. The samples were injected into the capillary by apressure pulse of 5 s×5 psi; the length of corresponding sample plug was4 mm as was calculated using the Poiseulle equation (Krylov et al. Anal.Chem. 2000, 72, 872). The capillary was rinsed with the run buffersolution for 2 minutes prior to each run. At the end of each run, thecapillary was rinsed with 100 mM NaOH for 2 minutes, followed by a rinsewith deionized water for 2 minutes.

Equilibrium mixtures of SSB, fDNA and SSB•fDNA complex were prepared bymixing solutions of 16 μM SSB and 205 nM fDNA in the run buffer at adesired volume ratio. The equilibrium mixtures were incubated atdifferent temperatures and electrophoretic runs were carried out atdifferent temperatures of the capillary. The areas of electrophoreticfeatures were determined and the values of K_(d), k_(off), and k_(or),were calculated as depicted in Panel A, using equations 13, 14, 10 and2. The values of K_(d) and k_(off) were plotted as functions oftemperature as shown in Panels B and C. Thermodynamic parameters,E_(a(off)), E_(a(on)), ΔH°, and ΔS° were then calculated using equations16-18:

$\begin{matrix}{E_{a{({on})}} = {E_{a{({off})}} - {\Delta\; H^{{^\circ}}}}} \\{= {63.\mspace{14mu}{kJ}\text{/}{mol}}} \\{{\ln\; k_{off}} = {{- \frac{E_{a{({off})}}}{R}}\frac{1}{T}}}\end{matrix}$E _(a(off)) R=slopeE _(a(off))=slope×R=6.0×10³×8.314≈50.kJ/molln K _(d)=−(ΔH°−TΔS°)/RT=−ΔH°/RT+ΔS°/RΔH°=−slope×R=−1.6×10³×8.314=−13.kJ/molΔS°=intercept×R=7.6×10⁻²×8.314==0.63 J/mol×K

Example 13 FIG. 8

Determination of Temperature Inside a Capillary during Electrophoresisusing Temperature-Dependence of Thermodynamic Parameters of ComplexFormation between SSB and fDNA.

In this example a CE instrument lacking capillary thermo-stabilizationwas used. The goal of this example was to determine the temperatureinside the capillary during electrophoresis. For this, thermodynamicdata obtained in example 12 (using a CE instrument withthermo-stabilized capillary) and the K_(d) value obtained in thisexample under conditions of unknown inner capillary temperature, wereused.

The temperature dependence of complex formation parameters for SSB andfDNA were used in this example to determine the unknown temperatureinside the capillary. NECEEM separation of SSB•fDNA complexes wasperformed using a laboratory-built CE instrument with fluorescencedetector described in detail elsewhere (Wu and Dovichi J. Chromatogr.1989, 480, 141). A 488 nm line of an Argon-ion laser was utilized toexcite the fluorescence of the fDNA. Uncoated fused silica capillariesof 40 cm×20 μm I.D.×150 μm O.D. were used. Electrophoresis was run witha positive electrode at the injection end biased at +16 kV. The runbuffer for NECEEM was 25.0 mM tetraborate at pH 9.4. The samples wereinjected into the capillary by a pressure pulse of 1 s×9.1 kPa; thelength of corresponding sample plug was 0.93 mm as was calculated usingthe Poiseulle equation (Krylov et al. Anal. Chem. 2000, 72, 872). Thecapillary was rinsed with the run buffer solution for 2 minutes prior toeach run. At the end of each run, the capillary was rinsed with 100 mMNaOH for 2 minutes, followed by a rinse with deionized water for 2minutes.

The NECEEM electropherograms obtained are identical to those depicted inFIG. 8. Therefore, this example is not accompanied by a graphicillustration. Using thermodynamic parameters, ΔH° and ΔS°, determined inexample 12, and K_(d) determined in this experiment, the temperatureinside of the capillary was calculated with the following equation:

$T = \frac{\Delta\; H^{{^\circ}}}{R\left( {{\Delta\; S^{{^\circ}}R} - {\ln\; K_{d}}} \right)}$The temperature inside the non-thermo-stabilized capillary was found tobe 35° C., that is 15° C. higher than the ambient temperature of 20° C.Using this method, the temperature can be determined in channels ofnon-thermo-stabilized microfabricated devices.

Example 14 FIG. 13

Determination of Unknown Concentration of Thrombin using its Aptamer.

In this example the use of a NECEEM-based method for the determinationof an unknown concentration of thrombin (T) using its aptamer, (L), isdemonstrated (Berezovski et al. Anal. Chem. 2003, 75, 1392). The aptamerwas fluorescently-labeled with fDNA. To facilitate this kind oflabeling, the aptamer was extended with a strand of DNA complementary tothe fDNA. FDNA formed a hybridization complex with the DNA extension onthe aptamer. The labeling procedure involved simply mixing the extendedaptamer with the fDNA. Since it is impossible to ensure an ideal 1:1ratio between the aptamer and fDNA while mixing, one of the componentsis present in excess and can be separated from the other.

NECEEM analysis of the thrombin•aptamer complex was performed using acommercial P/ACE MDQ apparatus (Beckman-Coulter) with fluorescencedetection. A 488 nm line of an Argon-ion laser was utilized to excitethe fluorescence of the fDNA. Uncoated fused silica capillaries of 40cm×20 μm I.D.×375 μm O.D. were used. Electrophoresis was carried outwith a positive electrode at the injection end biased at +16 kV. The runbuffer for NECEEM was 25.0 mM tetraborate supplemented with 100 nM SSBat pH 9.4. SSB served to enhance the separation of L from L•T. Thesamples were injected into the capillary by a pressure pulse of 5 s×5psi; the length of corresponding sample plug was 4 mm as was calculatedusing the Poiseulle equation (Krylov et al. Anal. Chem. 2000, 72, 872).The capillary was rinsed with the run buffer solution for 2 minutesprior to each run. At the end of each run, the capillary was rinsed with100 mM NaOH for 2 minutes, followed by a rinse with deionized water for2 minutes.

First, the K_(d) value of the thrombin•aptamer complex was determinedusing known concentrations of T and L by way of the approach describedin examples 2, 8, 9, and 10. The K_(d) value was found to be 2.4×10⁻⁷ M.Then, an unknown concentration of T was determined in a blindexperiment. For this, the equilibrium mixture containing the unknownconcentration of T and known concentration of L was prepared andsubjected to NECEEM. The areas under the peak and curve, A₁ and A₂, (seeFIG. 13) were determined and equation 19 was used to calculate theunknown concentration of thrombin.

The relative standard deviation of the method was 15%. The concentrationand mass limits of detection for thrombin quantitation were found to be60 nM and 7×10⁶ molecules, respectively. The dynamic range of the methodwas two orders of magnitude of thrombin concentration at a fixed aptamerconcentration of 61 nM.

Example 15 FIGS. 14-16

Selection of an Aptamer to PFTase from a Combinatorial Library ofOligonucleotides.

PFTase was used as a target to create aptamers from a combinatoriallibrary of DNA oligonucleotides.

The combinatorial library of DNA oligonucleotides was purchased from IDTTechnologies and contained two constant parts (16-mer and 20-mer) andone random part (35-mer with equal probability of all four nucleotidesA, T, C, and G): 5′-CCT GCC ACG CTC CGC TNN NNN NNN NNN NNN NNN NNN NNNNNN NNN NNN NNN TTC GAC ATG AGG CCC GGA TC-3′ (SEQ ID NO: 4), where Nrepresents a random nucleotide. All oligonucleotides in the library werefluorescently labeled by annealing the 16-mer constant part with acomplementary 15-mer oligonucleotide labeled with fluorescein (fDNA).

NECEEM separation of protein•DNA complexes was performed using acommercial P/ACE MDQ apparatus (Beckman-Coulter) with fluorescencedetection. A 488 nm line of an Argon-ion laser was utilized to excitethe fluorescence of the fDNA. Uncoated fused silica capillaries of 40cm×75 μm I.D.×375 μm O.D. were used. The distance from the injection endto the detector was 30 cm. Electrophoresis was run with a positiveelectrode at the injection end biased at +16 kV (400 V/cm). The runbuffer used for NECEEM was 25.0 mM tetraborate at pH 9.4. The sampleswere injected into the capillary by a pressure pulse of 5 s×0.5 psi; thelength of corresponding sample plug was 5 mm as was calculated using thePoiseulle equation (Krylov et al. Anal. Chem. 2000, 72, 872). Thecapillary was rinsed with the run buffer solution for 2 minutes prior toeach run. At the end of each run, the capillary was rinsed with 100 mMNaOH for 2 minutes, followed by a rinse with deionized water for 2minutes.

The migration time of the components of the PFTase sample was determinedusing UV detection (FIG. 14). This information was used to decide onwhich side of the sample peak aptamers had to be collected. The peaks ofPFTase were not detected during the selection procedure. The conditionsof electrophoresis were similar to those described above. Theconcentration of PFTase was 1 μM. It showed 4 components that could be:PFTase, its 2 subunits, and impurities. All 4 components were targetsfor selection of aptamers. All 4 components had a migration time shorterthan that of the combinatorial library (FIG. 15D). This allowed for thecollection of aptamers in the time window to the lets of the peak of thelibrary.

In the first step, the combinatorial library was mixed with the PFTasesample to give a final concentration of 1 μM for the library and 100 nMfor the PFTase. The incubation buffer contained 50 mM Tris-HCl at pH8.3, 10 mM MgCl₂, and 10 μM ZnCl₂. The equilibration time, t_(eq), was1000 s. The concentration of PFTase and the equilibration time definedthe upper limit of K_(d) and the lower limit of k_(on) for the aptamersselected: K_(d)<[PFTase]=1 μM and k_(on)>1/[PFTase]t_(eq)=1×10³ M⁻¹ s⁻¹.Accordingly, aptamers were selected for k_(off)=K_(d)k_(on)≈1×10⁻³ s⁻¹.The equilibrium mixture was then injected into the capillary and itscomponents were separated by NECEEM. The fraction from 0 to 8.8 minuteswas collected (FIG. 15A) and PCR amplified according to the followingprotocol. The PCR reaction mixture had a total volume of 100 μLincluding 10 μL of the fraction collected from NECEEM. The othercomponents of the PCR reaction mixture were: (i) 1 μM of each of twoprimers to the conserved terminal parts of the oligonucleotides (ii) 10mM Tris-HCl at pH 8.3, (iii) 50 mM KCl, (iv) 2.5 mM MgCl₂, (v) 200 nM ofeach of the four dNTPs, and (vi) 2.5 units of Taq DNA polymerase. EachPCR cycle consisted of a 30-second denaturation at 94° C., a 30-secondannealing at 55° C., and a 30-second extension at 72° C. PCR wasperformed for 30 cycles using a commercial Master Cycler apparatus(Eppendorf). A biotin moiety was incorporated into the 3′ PCR primerwhich allowed isolation of the nonbiotinylated strand of the PCRproducts using Affinitip streptavidin coated minicolumns (Hydros). AfterPCR amplification, ligands were mixed with the PFTase and subjected toan additional round of NECEEM. Two peaks representing complexes ofaptamers and two (of the four) components of the PFTase sample wereobserved after the very first step of selection (FIG. 15B). Thisequilibrium mixture was subjected to the second round of NECEEM.

In the second round, the pool of aptamers collected in the firstiteration, was mixed with the PFTase and subjected to NECEEM. Thefraction containing complexes of aptamers with components of the PFTasesample, was collected in the time window between 0 and 8.5 minutes. Thecollected pool of ligands was PCR amplified as described in the previousparagraph. It was then mixed with the PFTase and subjected to anadditional NECEEM. Four peaks corresponding to complexes of aptamerswith the four components of the PFTase sample were observed (FIG. 15C).The complexes were collected separately, as shown in FIG. 15C, and PCRamplified. As a result 4 aptamers were obtained for the 4 components ofthe PFTase sample. The identity of the fDNA peak was confirmed by addingSSB to the NECEEM run buffer. The peak of fDNA moved to shortermigration times while the migration times of the complexes did notchange (FIG. 16).

This example clearly demonstrates the usefulness of the NECEEM methodfor the selection of aptamers with specified ranges of bindingparameters, the use of the NECEEM method for the selection of aptamersfor multiple targets, and the use of SSB as a mediator in the separationof components of an equilibrium mixture subjected to NECEEM.

While the present invention has been described with reference to whatare presently considered to be the preferred examples, it is to beunderstood that the invention is not limited to the disclosed examples.To the contrary, the invention is intended to cover variousmodifications and equivalent arrangements included within the spirit andscope of the appended claims.

All publications, patents and patent applications are hereinincorporated by reference in their entirety to the same extent as ifeach individual publication, patent or patent application wasspecifically and individually indicated to be incorporated by referencein its entirety.

1. A homogenous method for determining the kinetic parameters of acomplex (L•T) formed between two components (L and T) wherein suchparameters are: (i) the equilibrium dissociation constant, K_(d), ofsaid complex (ii) the monomolecular rate constant, k_(off), of the decayof said complex (iii) the bimolecular rate constant, k_(on), of theformation of said complex wherein the method comprises: a) reacting saidcomponents under conditions that promote the formation of said complex,and allowing the reaction to come to equilibrium resulting in anequilibrium mixture; wherein said equilibrium mixture can be preparedinside the capillary or outside the capillary, wherein if saidequilibrium mixture is prepared outside the capillary a plug of saidequilibrium mixture is introduced into the capillary, wherein saidcapillary is a part of a capillary electrophoresis instrument; b)subjecting said equilibrium mixture to capillary electrophoresis undernon-equilibrium conditions to permit the decay of said complex andseparation of said components and complex; c) monitoring the migrationof one or more said components and said complex through a detectionpoint on or off the capillary to generate a migration pattern thereofincluding peaks and curves, the areas under which represent the amountsof said one or more components and/or complex that passed through saiddetection point; d) determining said equilibrium dissociation constantusing one of two following equations or their modifications:$K_{d} = \frac{A_{L}A_{T}}{A_{L \cdot T} + A_{decay}}$$K_{d} = \frac{{\lbrack T\rbrack_{0}\left( {1 + \frac{A_{L}}{A_{L \cdot T} + A_{decay}}} \right)} - \lbrack L\rbrack_{0}}{1 + {1/\frac{A_{L}}{A_{L \cdot T} + A_{decay}}}}$ wherein A_(L), A_(T), and A_(L•T) are normalized areas of said peakscorresponding to said components L and T and said complex L•T,respectively; A_(decay) is the area under one said curve correspondingto the decay of said complex L•T during said capillary electrophoresis;[T]₀ and [L]₀ are total concentrations of said components T and L in theequilibrium mixture, respectively; wherein the first equation isapplicable to cases when both L and T are detectable and the secondequation is applicable to cases when only one said component, L, isdetectable; e) determining said monomolecular rate constant by fittingone or more said curves of decay of said complex with asingle-exponential function:$I_{t} = {I_{t_{0}}\exp\left\{ {k_{off}\frac{t_{L \cdot T}}{t_{C} - t_{L \cdot T}}\left( {t - t_{0}} \right)} \right\}}$or  by:$k_{off} = \frac{\ln\left( {\left( {A_{L \cdot T} + A_{decay}} \right)/A_{L \cdot T}} \right)}{t_{L \cdot T}}$ wherein t₀ and t are initial and variable time points on said curve ofdecay of said complex, t_(C) is the migration of one of said components,whose signal constitutes said curve, and t_(L•T) is the migration timeof said complex in said capillary electrophoresis; f) determining saidbimolecular rate constant by:k _(on) =k _(off) /K _(d).
 2. The method of claim 1 wherein saidcomponents are a protein, peptide, enzyme, nucleic acid, biologicalsample, aptamer, organelle, cell, virus, particle or other reagentseparable by capillary electrophoresis.
 3. The method of claim 1 whereinany said component was pretreated by treatments including, lysis,freeze-thaw, centrifugation, enrichment or fractionation.
 4. The methodof claim 1 wherein one or multiple said components are detected byfluorescence, light absorbance, radioactive, electrochemical, mass orcharge detectors, or any combination of them; wherein said componentsare natively detectable and/or labeled with tags which are detectable bysaid detectors.
 5. The method of claim 1 wherein the parameters of saidcapillary electrophoresis are optimized by modifications to the voltage,temperature, composition and/or pH of the run buffer, capillarydimensions, the addition of mediators which enhance electrophoreticseparation, or capillary pretreatment.
 6. The method of claim 1 whereinsaid kinetic parameters are measured at different temperatures.
 7. Themethod of claim 6 wherein the method is used to determine thermodynamicparameters.
 8. The method of claim 7 wherein said thermodynamicparameters are used to measure the temperature in a capillary or otherelectrophoretic device.
 9. A homogeneous method for determining theconcentration of a target (T) using an affinity probe (L), comprised ofthe following steps: a) providing an equilibrium mixture of knownconcentrations of T and L, incubated for time (t) chosen by the operatorto reach equilibrium, prepared in a buffer that promotes efficientformation of complex between L and T; b) using the method of claim 1 todetermine the equilibrium dissociation constant of the formation of thecomplex L•T; c) preparing an equilibrium mixture comprised of unknownconcentration of T and known concentration of L; wherein saidequilibrium mixture can be prepared inside the capillary or outside thecapillary, wherein if said equilibrium mixture is prepared outside thecapillary a plug of said equilibrium mixture is introduced into saidcapillary; wherein said capillary is a part of a capillaryelectrophoresis instrument; d) separating components and complexes bycapillary electrophoresis under non-equilibrium conditions optimized bythe operator to separate the complex L•T from L; e) tracking L and L•Tusing a detector capable of generating an electropherogram of themigration pattern of the components including peaks and curves; f)analyzing peaks and curves to determine the concentration of T usingequation:$\lbrack T\rbrack_{0} = {{K_{d}/\frac{A_{L}}{A_{L \cdot T} + A_{decay}}} + {\lbrack L\rbrack_{0}/\left( {1 + \frac{A_{L}}{A_{L \cdot T} + A_{decay}}} \right)}}$ wherein A_(L) and A_(L•T) are areas of said peaks corresponding to Land L•T, respectively; A_(decay) is the area under one said curvecorresponding to the decay of said complex L•T during said capillaryelectrophoresis; [T]₀ and [L]₀ are total concentrations of the twocomponents in said equilibrium mixture.
 10. The method of claim 9wherein L and T can be are any of the following: a protein, peptide,enzyme, nucleic acid, aptamer, organelle, cell, virus, combinatoriallibrary, patient sample, biological sample, particle or other reagentseparable by capillary electrophoresis.
 11. The method of claim 9wherein L or T or both are pretreated by treatments including but notlimited to: purification, lysis, freeze-thaw, centrifugation, enrichmentor fractionation.
 12. The method of claim 9 wherein the parameters ofsaid capillary electrophoresis are optimized by modifications to thevoltage, temperature, composition and/or pH of the run buffer, capillarydimensions, the addition of mediators which enhance electrophoreticseparation, or capillary pretreatment.
 13. The method of claim 9 whereinthe calibration curve is built and used instead of determining and usingsaid equilibrium dissociation constant and said equation.
 14. The methodof claim 9 wherein T is a protein and L is an aptamer.
 15. The method ofclaim 9 wherein the method is used as a diagnostic tool to measure theconcentration of T present in a patient or biological sample.
 16. Themethod of claim 5 wherein the capillary pretreatment is siliconization.17. The method of claim 10 wherein the combinatorial library comprisespeptides, nucleic acids or organic molecules.
 18. The method of claim 12wherein the capillary pretreatment is siliconization.